• Compact composition operators with non-linear symbols on the H2 space of Dirichlet series 

      Bayart, Frederic; Brevig, Ole Fredrik (Journal article; Peer reviewed, 2017)
      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, ...
    • Composition operators and embedding theorems for some function spaces of Dirichlet series 

      Bayart, Frederic; Brevig, Ole Fredrik (Journal article; Peer reviewed, 2019)
      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 on Bohr-Bergman spaces of Dirichlet series 

      Brevig, Ole Fredrik; Bailleul, Maxime (Journal article; Peer reviewed, 2016)
      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 ...
    • Contractive inequalities for Bergman spaces and multiplicative Hankel forms 

      Bayart, Frédéric; Brevig, Ole Fredrik; Haimi, Antti; Ortega-Cerdà, Joaquim; Perfekt, Karl-Mikael (Journal article; Peer reviewed, 2019)
      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 ...
    • Contractive inequalities for Hardy spaces 

      Brevig, Ole Fredrik; Ortega-Cerdà, Joaquim; Seip, Kristian; Zhao, Jing (Journal article; Peer reviewed, 2018)
      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 ...
    • Hankel forms and Nehari's theorem 

      Søvik, Øistein (Master thesis, 2017)
      The purpose of this thesis is to explore the relation between the classical Hardy space of analytic functions and the Hardy space of Dirichlet series. Two chapters are devoted to developing the basic properties of these ...
    • High pseudomoments of the Riemann zeta function 

      Brevig, Ole Fredrik; Heap, Winston (Journal article, 2018)
      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 ...
    • Linear functions and duality on the infinite polytorus 

      Brevig, Ole Fredrik (Journal article; Peer reviewed, 2019)
      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.
    • Linear space properties of H^p spaces of Dirichlet series 

      Bondarenko, Andrii; Brevig, Ole Fredrik; Saksman, Eero; Seip, Kristian (Journal article; Peer reviewed, 2019)
      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, ...
    • Norms of composition operators on the $H^2$ space of Dirichlet series 

      Brevig, Ole Fredrik; Perfekt, Karl-Mikael (Journal article; Peer reviewed, 2020)
      , 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 ...
    • Operator theory in spaces of Dirichlet series 

      Brevig, Ole Fredrik (Doctoral theses at NTNU;2017:193, Doctoral thesis, 2017)
    • Pseudomoments of the Riemann zeta function 

      Bondarenko, Andrii; Brevig, Ole Fredrik; Saksman, Eero; Seip, Kristian; Zhao, Jing (Journal article; Peer reviewed, 2018)
      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 ...
    • Sharp norm estimates for composition operators and Hilbert-type inequalities 

      Brevig, Ole Fredrik (Journal article; Peer reviewed, 2017)
      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 multiplicative Hilbert matrix 

      Brevig, Ole Fredrik; Perfekt, Karl-Mikael; Seip, Kristian; Siskakis, Aristomenis; Vukotic, Dragan (Journal article; Peer reviewed, 2016)
    • The Sidon Constant for Ordinary Dirichlet Series 

      Brevig, Ole Fredrik (Master thesis, 2013)
      We obtain the asymptotic formula of the Sidon constant for ordinary Dirichlet series using the Bohnenblust--Hille inequality and estimates on smooth numbers. We moreover give precise estimates for the error term.
    • Volterra operators on Hardy spaces of Dirichlet series 

      Brevig, Ole Fredrik; Perfekt, Karl-Mikael; Seip, Kristian (Journal article; Peer reviewed, 2019)
      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 ...