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• Brevig, Ole Fredrik; Llinares, Adrián & Seip, Kristian (2026). Critical Exponents of the Riesz Projection. Computational methods in Function Theory. ISSN 1617-9447. 26(1), s. 123–140. doi: 10.1007/s40315-024-00566-z. Fulltekst i vitenarkiv
• Brevig, Ole Fredrik (2025). Two footnotes to the F. & M. Riesz theorem. Annales Fennici Mathematici. ISSN 2737-0690. 50(2), s. 459–466. doi: 10.54330/afm.163565. Fulltekst i vitenarkiv Vis sammendrag

  We present a new proof of the F. & M. Riesz theorem on analytic measures of the unit circle \(\mathbb{T}\) that is based the following elementary inequality: If \(f\) is analytic in the unit disc \(\mathbb{D}\) and \(0 \leq r \leq \varrho < 1\), then \(\|f_r-f_\varrho\|_1 \leq 2 \sqrt{\|f_\varrho\|_1^2-\|f_r\|_1^2}\), where \(f_r(e^{i\theta})=f(r e^{i\theta})\) and where \(\|\cdot\|_1\) denotes the norm of \(L^1(\mathbb{T})\). The proof extends to the infinite-dimensional torus \(\mathbb{T}^\infty\), where it clarifies the relationship between Hilbert's criterion for \(H^1(\mathbb{T}^\infty)\) and the F. & M. Riesz theorem.

• Brevig, Ole Fredrik; Kouroupis, Athanasios & Perfekt, Karl-Mikael (2025). Almost periodicity and boundary values of Dirichlet series. Transactions of the American Mathematical Society. ISSN 0002-9947. 378, s. 5677–5700. doi: 10.1090/tran/9420. Fulltekst i vitenarkiv Vis sammendrag

  We employ almost periodicity to establish analogues of the Hardy–Stein identity and the Littlewood–Paley formula for Hardy spaces of Dirichlet series. A construction of Saksman and Seip shows that the limits in this Littlewood–Paley formula cannot be interchanged. We apply this construction to show that the limits in the definition of the mean counting function for Dirichlet series cannot be interchanged. These are essentially statements about the two different kinds of boundary values that we associate with Dirichlet series that converge to a bounded analytic function in a half-plane. The treatment of the mean counting function also involves an investigation of the zero sets and Blaschke products of such Dirichlet series.

• Brevig, Ole Fredrik; Chirre, Andrés; Ortega-Cerdà, Joaquim & Seip, Kristian (2024). Point evaluation in Paley–Wiener spaces. Journal d'Analyse Mathematique. ISSN 0021-7670. 153(2), s. 595–670. doi: 10.1007/s11854-024-0338-z. Fulltekst i vitenarkiv
• Brevig, Ole Fredrik & Seip, Kristian (2024). The norm of the backward shift on H1 is 2/sqrt(3). Pure and Applied Functional Analysis. ISSN 2189-3756. 9(4), s. 991–994. Fulltekst i vitenarkiv
• Brevig, Ole Fredrik & Seip, Kristian (2024). Maximal norm Hankel operators. Journal of Mathematical Analysis and Applications. ISSN 0022-247X. 529(2). doi: 10.1016/j.jmaa.2023.127221. Fulltekst i vitenarkiv
• Brevig, Ole Fredrik (2024). The best constant in a Hilbert-type inequality. Expositiones mathematicae. ISSN 0723-0869. 42(1). doi: 10.1016/j.exmath.2023.125530. Fulltekst i vitenarkiv
• Brevig, Ole Fredrik & Kouroupis, Athanasios (2024). An extension of Bohr's theorem. Proceedings of the American Mathematical Society. ISSN 0002-9939. 152(1), s. 371–374. doi: 10.1090/proc/16622. Fulltekst i vitenarkiv
• Bampouras, Konstantinos & Brevig, Ole Fredrik (2024). Norm attaining vectors and Hilbert points. Studia Mathematica. ISSN 0039-3223. 276(2), s. 157–169. doi: 10.4064/sm231128-7-2. Fulltekst i vitenarkiv Vis sammendrag

  Let H be a Hilbert space that can be embedded as a dense subspace of a Banach space X such that the norm of the embedding is equal to 1. We consider the following statements for a nonzero vector φ in H: (A) ∥φ∥X =∥φ∥H. (H) ∥φ+f∥X ≥∥φ∥X for every f in H such that ⟨f,φ⟩ = 0. We use duality arguments to establish that (A) =⇒ (H), before turning our attention to the special case when the Hilbert space in question is the Hardy space H2(Td) and the Banach space is either the Hardy space H1(Td) or the weak product space H2(Td)⊙H2(Td). If d = 1, then the two Banach spaces are equal and it is known that (H) =⇒ (A). If d ≥ 2, then the Banach spaces do not coincide and a case study of the polynomials φα(z) = z2 1 +αz1z2 +z2 2 for α ≥ 0 illustrates that the statements (A) and (H) for the two Banach spaces describe four distinct sets of functions.

• Brevig, Ole Fredrik & Perfekt, Karl-Mikael (2023). The Nehari problem for the Paley--Wiener space of a disc. Journal of Geometric Analysis. ISSN 1050-6926. 33(1). doi: 10.1007/s12220-022-01063-2. Fulltekst i vitenarkiv Vis sammendrag

  There is a bounded Hankel operator on the Paley–Wiener space of a disc in R2 which does not arise from a bounded symbol.

• Brevig, Ole Fredrik; Ortega-Cerdà, Joaquim & Seip, Kristian (2023). Hilbert points in Hardy spaces. St. Petersburg Mathematical Journal. ISSN 1061-0022. 34(3), s. 405–425. doi: 10.1090/spmj/1760. Fulltekst i vitenarkiv
• Brevig, Ole Fredrik; Perfekt, Karl-Mikael & Pushnitski, Alexander (2023). The spectrum of some Hardy kernel matrices. Annales de l'Institut Fourier. ISSN 0373-0956. 74(3), s. 1061–1094. doi: 10.5802/aif.3589. Fulltekst i vitenarkiv
• Brevig, Ole Fredrik & Grepstad, Sigrid (2023). Hilbert points in Hilbert space-valued L^p spaces. North-Western European Journal of Mathematics. ISSN 2496-5170. 9, s. 17–29. Fulltekst i vitenarkiv Vis sammendrag

  Let H be a Hilbert space and (Ω,F ,µ) a probability space. A Hilbert point in L p (Ω;H) is a nontrivial function ϕ such that ∥ϕ∥p ≤ ∥ϕ+f ∥p whenever ⟨f ,ϕ⟩ = 0. We demonstrate that ϕ is a Hilbert point in L p (Ω;H) for some p , 2 if and only if ∥ϕ(ω)∥H assumes only the two values 0 and C > 0. We also obtain a geometric description of when a sum of independent Rademacher variables is a Hilbert point.

• Brevig, Ole Fredrik & Perfekt, Karl-Mikael (2022). Orthogonal decomposition of composition operators on the $H^2$ space of Dirichlet series. Journal of Functional Analysis. ISSN 0022-1236. 282(5). doi: 10.1016/j.jfa.2021.109353. Fulltekst i vitenarkiv Vis sammendrag

  Let denote the Hilbert space of Dirichlet series with square-summable coefficients. We study composition operators on which are generated by symbols of the form , in the case that . If only a subset of prime numbers features in the Dirichlet series of φ, then the operator admits an associated orthogonal decomposition. Under sparseness assumptions on we use this to asymptotically estimate the approximation numbers of . Furthermore, in the case that φ is supported on a single prime number, we affirmatively settle the problem of describing the compactness of in terms of the ordinary Nevanlinna counting function. We give detailed applications of our results to affine symbols and to angle maps.

• Brevig, Ole Fredrik (2022). Minimal norm Hankel operators. Proceedings of the American Mathematical Society. ISSN 0002-9939. 150(10), s. 4383–4391. doi: 10.1090/proc/15969. Fulltekst i vitenarkiv
• Brevig, Ole Fredrik; Grepstad, Sigrid & Instanes, Sarah May (2022). F. Wiener’s Trick and an Extremal Problem for H^p. Computational methods in Function Theory. ISSN 1617-9447. 23(4), s. 697–722. doi: 10.1007/s40315-022-00469-x. Fulltekst i vitenarkiv Vis sammendrag

  For 0<p≤∞, let Hp denote the classical Hardy space of the unit disc. We consider the extremal problem of maximizing the modulus of the kth Taylor coefficient of a function f∈Hp which satisfies ∥f∥Hp≤1 and f(0)=t for some 0≤t≤1. In particular, we provide a complete solution to this problem for k=1 and 0<p<1. We also study F. Wiener’s trick, which plays a crucial role in various coefficient-related extremal problems for Hardy spaces.

• Brevig, Ole Fredrik & Perfekt, Karl-Mikael (2021). A mean counting function for Dirichlet series and compact composition operators. Advances in Mathematics. ISSN 0001-8708. 385. doi: 10.1016/j.aim.2021.107775. Fulltekst i vitenarkiv Vis sammendrag

  We introduce a mean counting function for Dirichlet series, which plays the same role in the function theory of Hardy spaces of Dirichlet series as the Nevanlinna counting function does in the classical theory. The existence of the mean counting function is related to Jessen and Tornehave's resolution of the Lagrange mean motion problem. We use the mean counting function to describe all compact composition operators with Dirichlet series symbols on the Hardy–Hilbert space of Dirichlet series, thus resolving a problem which has been open since the bounded composition operators were described by Gordon and Hedenmalm. The main result is that such a composition operator is compact if and only if the mean counting function of its symbol satisfies a decay condition at the boundary of a half-plane.

• Brevig, Ole Fredrik; Ortega-Cerdà, Joaquim & Seip, Kristian (2021). Idempotent Fourier multipliers acting contractively on H^p spaces. Geometric and Functional Analysis. ISSN 1016-443X. 31(6), s. 1377–1413. doi: 10.1007/s00039-021-00586-0. Fulltekst i vitenarkiv Vis sammendrag

  We describe the idempotent Fourier multipliers that act contractively on Hp spaces of the d-dimensional torus Td for d≥1 and 1≤p≤∞. When p is not an even integer, such multipliers are just restrictions of contractive idempotent multipliers on Lp spaces, which in turn can be described by suitably combining results of Rudin and Andô. When p=2(n+1), with n a positive integer, contractivity depends in an interesting geometric way on n, d, and the dimension of the set of frequencies associated with the multiplier. Our results allow us to construct a linear operator that is densely defined on Hp(T∞) for every 1≤p≤∞ and that extends to a bounded operator if and only if p=2,4,…,2(n+1).

• Brevig, Ole Fredrik; Ortega-Cerdà, Joaquim & Seip, Kristian (2021). A converse to the Schwarz lemma for planar harmonic maps. Journal of Mathematical Analysis and Applications. ISSN 0022-247X. 497(2). doi: 10.1016/j.jmaa.2020.124908. Fulltekst i vitenarkiv Vis sammendrag

  A sharp version of a recent inequality of Kovalev and Yang on the ratio of the (H1)∗ and H4 norms for certain polynomials is obtained. The inequality is applied to establish a sharp and tractable sufficient condition for the Wirtinger derivatives at the origin for harmonic self-maps of the unit disc which fix the origin.

• Brevig, Ole Fredrik & Miheisi, Nazar (2021). Projecting onto Helson matrices in Schatten classes. Studia Mathematica. ISSN 0039-3223. 256(1), s. 109–119. doi: 10.4064/SM190901-24-3. Fulltekst i vitenarkiv Vis sammendrag

  A Helson matrix is an infinite matrix A=(am,n)m,n≥1 such that the entry am,n depends only on the product mn. We demonstrate that the orthogonal projection from the Hilbert–Schmidt class S2 onto the subspace of Hilbert–Schmidt Helson matrices does not extend to a bounded operator on the Schatten class Sq for 1≤q≠2<∞. In fact, we prove a more general result showing that a large class of natural projections onto Helson matrices are unbounded in the Sq-norm for 1≤q≠2<∞. Two additional results are also presented.

• Brevig, Ole Fredrik & Saksman, Eero (2020). Coefficient estimates for Hp spaces with 0<p<1. Proceedings of the American Mathematical Society. ISSN 0002-9939. 148(9), s. 3911–3924. doi: 10.1090/proc/14995. Fulltekst i vitenarkiv Vis sammendrag

  Let C(k,p) denote the smallest real number such that the estimate |ak| ≤C(k,p)‖f‖Hp holds for every f(z) =∑n≥0anzn in the Hp space of the unit disc. We compute C(2,p)for0<p<1andC(3,2/3), and identify the functions attaining equality in the estimate.

• Brevig, Ole Fredrik & Perfekt, Karl-Mikael (2020). Norms of composition operators on the $H^2$ space of Dirichlet series. Journal of Functional Analysis. ISSN 0022-1236. 278(2). doi: 10.1016/j.jfa.2019.108320. Fulltekst i vitenarkiv Vis sammendrag

  , generated by Dirichlet series symbols φ. We prove two different subordination principles for such operators. One concerns affine symbols only, and is based on an arithmetical condition on the coefficients of φ. The other concerns general symbols, and is based on a geometrical condition on the boundary values of φ. Both principles are strict, in the sense that they characterize the composition operators of maximal norm generated by symbols having given mapping properties. In particular, we generalize a result of J.H. Shapiro on the norm of composition operators on the classical Hardy space of the unit disc. Based on our techniques, we also improve the recently established upper and lower norm bounds in the special case that

• Brevig, Ole Fredrik; Perfekt, Karl-Mikael & Seip, Kristian (2019). Volterra operators on Hardy spaces of Dirichlet series. Journal für die Reine und Angewandte Mathematik. ISSN 0075-4102. 2019(754), s. 179–223. doi: 10.1515/crelle-2016-0069. Fulltekst i vitenarkiv Vis sammendrag

  For a Dirichlet series symbol g.s/ D P n 1 bnn s , the associated Volterra operator Tg acting on a Dirichlet series f .s/ D P n 1 ann s is defined by the integral f 7! Z C1 s f .w/g0 .w/ dw: We show that Tg is a bounded operator on the Hardy space Hp of Dirichlet series with 0 < p < 1 if and only if the symbol g satisfies a Carleson measure condition. When appropriately restricted to one complex variable, our condition coincides with the standard Carleson measure characterization of BMOA.D/. A further analogy with classical BMO is that exp.cjgj/ is integrable (on the infinite polytorus) for some c > 0 whenever Tg is bounded. In particular, such g belong to Hp for every p < 1. We relate the boundedness of Tg to several other BMO-type spaces: BMOA in half-planes, the dual of H1 , and the space of symbols of bounded Hankel forms. Moreover, we study symbols whose coefficients enjoy a multiplicative structure and obtain coefficient estimates for m-homogeneous symbols as well as for general symbols. Finally, we consider the action of Tg on reproducing kernels for appropriate sequences of subspaces of H2 . Our proofs employ function and operator theoretic techniques in one and several variables; a variety of number theoretic arguments are used throughout the paper in our study of special classes of symbols

• Brevig, Ole Fredrik (2019). Linear functions and duality on the infinite polytorus. Collectanea Mathematica. ISSN 0010-0757. 70(3), s. 493–500. doi: 10.1007/s13348-019-00243-8. Fulltekst i vitenarkiv Vis sammendrag

  We consider the following question: are there exponents 22 . Our approach is based on duality arguments and a detailed study of linear functions. Some related results are also presented.

• Bondarenko, Andrii; Brevig, Ole Fredrik; Saksman, Eero & Seip, Kristian (2019). Linear space properties of H^p spaces of Dirichlet series. Transactions of the American Mathematical Society. ISSN 0002-9947. 372(9), s. 6677–6702. doi: 10.1090/tran/7898. Fulltekst i vitenarkiv Vis sammendrag

  We study H p spaces of Dirichlet series, called H p , for the range 0 < p < ∞. We begin by showing that two natural ways to define H p coincide. We then proceed to study some linear space properties of H p . More specifically, we study linear functionals generated by fractional primitives of the Riemann zeta function; our estimates rely on certain Hardy–Littlewood inequalities and display an interesting phenomenon, called contractive symmetry between H p and H 4/p , contrasting the usual L p duality. We next deduce general coefficient estimates, based on an interplay between the multiplicative structure of H p and certain new one variable bounds. Finally, we deduce general estimates for the norm of the partial sum operator P∞ n=1 ann −s 7→ PN n=1 ann −s on H p with 0 < p ≤ 1, supplementing a classical result of Helson for the range 1 < p < ∞. The results for the coefficient estimates and for the partial sum operator exhibit the traditional schism between the ranges 1 ≤ p ≤ ∞ and 0 < p < 1.

• Bayart, Frédéric; Brevig, Ole Fredrik; Haimi, Antti; Ortega-Cerdà, Joaquim & Perfekt, Karl-Mikael (2019). Contractive inequalities for Bergman spaces and multiplicative Hankel forms. Transactions of the American Mathematical Society. ISSN 0002-9947. 371(1), s. 681–707. doi: 10.1090/tran/7290. Fulltekst i vitenarkiv Vis sammendrag

  We consider sharp inequalities for Bergman spaces of the unit disc, establishing analogues of the inequality in Carleman's proof of the isoperimetric inequality and of Weissler's inequality for dilations. By contractivity and a standard tensorization procedure, the unit disc inequalities yield corresponding inequalities for the Bergman spaces of Dirichlet series. We use these results to study weighted multiplicative Hankel forms associated with the Bergman spaces of Dirichlet series, reproducing most of the known results on multiplicative Hankel forms associated with the Hardy spaces of Dirichlet series. In addition, we find a direct relationship between the two types of forms which does not exist in lower dimensions. Finally, we produce some counterexamples concerning Carleson measures on the infinite polydisc.

• Bayart, Frederic & Brevig, Ole Fredrik (2019). Composition operators and embedding theorems for some function spaces of Dirichlet series. Mathematische Zeitschrift. ISSN 0025-5874. 293(3-4), s. 989–1014. doi: 10.1007/s00209-018-2215-x. Fulltekst i vitenarkiv Vis sammendrag

  We observe that local embedding problems for certain Hardy and Bergman spaces of Dirichlet series are equivalent to boundedness of a class of composition operators. Following this, we perform a careful study of such composition operators generated by polynomial symbols \varphi on a scale of Bergman-type Hilbert spaces \mathscr {D}_\alpha. We investigate the optimal \beta such that the composition operator \mathscr {C}_\varphi maps \mathscr {D}_\alpha boundedly into \mathscr {D}_\beta. We also prove a new embedding theorem for the non-Hilbertian Hardy space \mathscr {H}^p into a Bergman space in the half-plane and use it to consider composition operators generated by polynomial symbols on \mathscr {H}^p, finding the first non-trivial results of this type. The embedding also yields a new result for the functional associated to the multiplicative Hilbert matrix.

• Brevig, Ole Fredrik & Heap, Winston (2019). High pseudomoments of the Riemann zeta function. Journal of Number Theory. ISSN 0022-314X. 197, s. 383–410. doi: 10.1016/j.jnt.2018.10.001. Fulltekst i vitenarkiv Vis sammendrag

  The pseudomoments of the Riemann zeta function, denoted Mk(N), are defined as the 2kth integral moments of the Nth partial sum of ζ(s) on the critical line. We improve the upper and lower bounds for the constants in the estimate Mk(N) ≍k (log N) k 2 as N → ∞ for fixed k ≥ 1, thereby determining the two first terms of the asymptotic expansion. We also investigate uniform ranges of k where this improved estimate holds and when Mk(N) may be lower bounded by the 2kth power of the L ∞ norm of the Nth partial sum of ζ(s) on the critical line.

• Bondarenko, Andrii; Brevig, Ole Fredrik; Saksman, Eero; Seip, Kristian & Zhao, Jing (2018). Pseudomoments of the Riemann zeta function. Bulletin of the London Mathematical Society. ISSN 0024-6093. 50(4), s. 709–724. doi: 10.1112/blms.12183. Fulltekst i vitenarkiv Vis sammendrag

  The 2kth pseudomoments of the Riemann zeta function ζ ( s ) are, following Conrey and Gamburd, the 2 k th integral moments of the partial sums of ζ ( s ) on the critical line. For fixed k > 1 / 2 , these moments are known to grow like ( log N ) k 2 , where N is the length of the partial sum, but the true order of magnitude remains unknown when k ⩽ 1 / 2 . We deduce new Hardy–Littlewood inequalities and apply one of them to improve on an earlier asymptotic estimate when k → ∞ . In the case k < 1 / 2 , we consider pseudomoments of ζ α ( s ) for α > 1 and the question of whether the lower bound ( log N) k 2 α 2 known from earlier work yields the true growth rate. Using ideas from recent work of Harper, Nikeghbali and Radziwiłł and some probabilistic estimates of Harper, we obtain the somewhat unexpected result that these pseudomements are bounded below by log N to a power larger than k 2 α 2 when k < 1 / e and N is sufficiently large.

• Brevig, Ole Fredrik; Ortega-Cerdà, Joaquim; Seip, Kristian & Zhao, Jing (2018). Contractive inequalities for Hardy spaces. Functiones et Approximatio Commentarii Mathematici. ISSN 0208-6573. 59(1), s. 41–56. doi: 10.7169/facm/1680. Fulltekst i vitenarkiv Vis sammendrag

  We state and discuss several interrelated results, conjectures, and questions regarding contractive inequalities for classical Hp spaces of the unit disc. We study both coefficient estimates in terms of weighted ℓ 2 sums and the Riesz projection viewed as a map from L q to Hp with q ≥ p. Some numerical evidence is given that supports our conjectures.

• Brevig, Ole Fredrik (2017). Sharp norm estimates for composition operators and Hilbert-type inequalities. Bulletin of the London Mathematical Society. ISSN 0024-6093. 49(6), s. 965–978. doi: 10.1112/blms.12092. Fulltekst i vitenarkiv Vis sammendrag

  Let H 2 denote the Hardy space of Dirichlet series f ( s ) = ∑ n ⩾ 1 a n n − s with square summable coefficients and suppose that φ is a symbol generating a composition operator on H 2 by C φ ( f ) = f ∘ φ . Let ζ denote the Riemann zeta function and α 0 = 1.48 … the unique positive solution of the equation α ζ ( 1 + α ) = 2 . We obtain sharp upper bounds for the norm of C φ on H 2 when 0 < Re φ ( + ∞ ) − 1 / 2 ⩽ α 0 , by relating such sharp upper bounds to the best constant in a family of discrete Hilbert‐type inequalities.

• Bayart, Frederic & Brevig, Ole Fredrik (2017). Compact composition operators with non-linear symbols on the $H^2$ space of Dirichlet series. Pacific Journal of Mathematics. ISSN 0030-8730. 291(1), s. 81–120. doi: 10.2140/pjm.2017.291.81. Fulltekst i vitenarkiv Vis sammendrag

  We investigate compactness of composition operators on the Hardy space of Dirichlet series induced by a map φ(s)=c0s+φ0(s), where φ0 is a Dirichlet polynomial. Our results depend heavily on the characteristic c0 of φ and, whenc0=0, on both the degree of φ0 and its local behavior near a boundary point. We also study the approximation numbers for some of these operators. Our methods involve geometric estimates of Carleson measures and tools from differential geometry.

• Brevig, Ole Fredrik & Perfekt, Karl-Mikael (2016). Weak Product Spaces of Dirichlet Series. Integral equations and operator theory. ISSN 0378-620X. 86(4), s. 453–473. doi: 10.1007/s00020-016-2320-3. Fulltekst i vitenarkiv
• Brevig, Ole Fredrik & Heap, Winston Paul (2016). Convergence abscissas for Dirichlet series with multiplicative coefficients. Expositiones mathematicae. ISSN 0723-0869. 34(4), s. 448–453. doi: 10.1016/j.exmath.2015.10.005. Fulltekst i vitenarkiv
• Brevig, Ole Fredrik & Bailleul, Maxime (2016). Composition operators on Bohr-Bergman spaces of Dirichlet series. Annales Academiae Scientiarum Fennicae Mathematica. ISSN 1239-629X. 41(1), s. 129–142. doi: 10.5186/aasfm.2016.4104. Fulltekst i vitenarkiv Vis sammendrag

  For α ∈ R, let Dα denote the scale of Hilbert spaces consisting of Dirichlet series f(s) = P∞ n=1 ann −s that satisfy P∞ n=1 |an| 2/[d(n)]α < ∞. The Gordon–Hedenmalm Theorem on composition operators for H 2 = D0 is extended to the Bergman case α > 0. These composition operators are generated by functions of the form Φ(s) = c0s+ϕ(s), where c0 is a nonnegative integer and ϕ(s) is a Dirichlet series with certain convergence and mapping properties. For the operators with c0 = 0 a new phenomenon is discovered: If 0 < α < 1, the space Dα is mapped by the composition operator into a smaller space in the same scale. When α > 1, the space Dα is mapped into a larger space in the same scale. Moreover, a partial description of the composition operators on the Dirichlet–Bergman spaces A p for 1 ≤ p < ∞ are obtained, in addition to new partial results for composition operators on the Dirichlet–Hardy spaces H p when p is an odd integer.

• Brevig, Ole Fredrik (2016). Zeros of functions in Bergman-type Hilbert spaces of Dirichlet series. Mathematica Scandinavica. ISSN 0025-5521. 119(2), s. 237–248. doi: 10.7146/math.scand.a-24745. Fulltekst i vitenarkiv
• Brevig, Ole Fredrik; Perfekt, Karl-Mikael; Seip, Kristian; Siskakis, Aristomenis & Vukotic, Dragan (2016). The multiplicative Hilbert matrix. Advances in Mathematics. ISSN 0001-8708. 302, s. 410–432. doi: 10.1016/j.aim.2016.07.019. Fulltekst i vitenarkiv
• Brevig, Ole Fredrik (2016). An embedding constant for the Hardy space of Dirichlet series. Proceedings of the American Mathematical Society. ISSN 0002-9939. 145(4), s. 1639–1641. doi: 10.1090/proc/13330. Fulltekst i vitenarkiv
• Brevig, Ole Fredrik & Perfekt, Karl-Mikael (2015). Failure of Nehari's theorem for multiplicative Hankel forms in Schatten classes. Studia Mathematica. ISSN 0039-3223. 228(2), s. 101–108. doi: 10.4064/sm228-2-1. Fulltekst i vitenarkiv
• Brevig, Ole Fredrik (2014). On the Sidon constant for Dirichlet polynomials. Bulletin des Sciences Mathématiques. ISSN 0007-4497. 138(5), s. 656–664. doi: 10.1016/j.bulsci.2013.12.002. Fulltekst i vitenarkiv

Se alle arbeider i NVA

• Brevig, Ole Fredrik (2026). Norms of composition operators on the Hardy space of Dirichlet series. Fulltekst i vitenarkiv Vis sammendrag

  I will discuss several interconnected problems about composition operators on the Hardy space of Dirichlet series that concern the relationship between the norm of the composition operator and the geometric properties of its symbol. Some results align well with corresponding results for the classical Hardy space in the unit disc, while for other results we discover new phenomena.

• Brevig, Ole Fredrik (2025). Two results concerning H^1. Fulltekst i vitenarkiv Vis sammendrag

  I will discuss two related results concerning the classical Hardy space H^1 of the unit disc. The first result is an effective version of Fatou's theorem, which can be used to prove the F. & M. Riesz theorem. The second result pertains to the norm of the backward shift operator. Based on joint work with Kristian Seip.

• Brevig, Ole Fredrik (2023). Corrigendum: Sharp norm estimates for composition operators and Hilbert-type inequalities. Bulletin of the London Mathematical Society. ISSN 0024-6093. 49(6), s. 965–978. doi: 10.1112/blms.12938. Fulltekst i vitenarkiv
• Brevig, Ole Fredrik & Perfekt, Karl-Mikael (2023). Correction to: Weak Product Spaces of Dirichlet Series. Integral equations and operator theory. ISSN 0378-620X. 95(3). doi: 10.1007/s00020-023-02736-5. Fulltekst i vitenarkiv

Se alle arbeider i NVA