Browsing NTNU Open by Author "Brevig, Ole Fredrik"
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Coefficient estimates for $H^p$ spaces with $0<p<1$
Brevig, Ole Fredrik; Saksman, Eero (Peer reviewed; Journal article, 2020)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 ... 
Compact composition operators with nonlinear 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 BohrBergman 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; OrtegaCerdà, Joaquim; Perfekt, KarlMikael (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; OrtegaCerdà, 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 ... 
A converse to the Schwarz lemma for planar harmonic maps
Brevig, Ole Fredrik; OrtegaCerdà, Joaquim; Seip, Kristian (Peer reviewed; Journal article, 2021)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 ... 
An extension of Bohr's theorem
Brevig, Ole Fredrik; Kouroupis, Athanasios (Peer reviewed; Journal article, 2024) 
F. Wiener’s Trick and an Extremal Problem for H<sup>p</sup>
Brevig, Ole Fredrik; Grepstad, Sigrid; Instanes, Sarah May (Peer reviewed; Journal article, 2022)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 ... 
Faktorisering i Hardyrom
Instanes, Sarah May (Bachelor thesis, 2020)Vi definerer Blaschkeprodukt og viser Rieszfaktoriseringen for funksjoner i Hardyrom. Dette bruker vi til å vise den isoperimetriske ulikheten. 
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 ... 
Hilbert points in Hardy spaces
Brevig, Ole Fredrik; OrtegaCerdà, Joaquim; Seip, Kristian (Peer reviewed; Journal article, 2023) 
Hilbert points in Hilbert spacevalued $L^p$ spaces
Brevig, Ole Fredrik; Grepstad, Sigrid (Peer reviewed; Journal article, 2023)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 ... 
Idempotent Fourier multipliers acting contractively on Hp spaces
Brevig, Ole Fredrik; OrtegaCerdà, Joaquim; Seip, Kristian (Peer reviewed; Journal article, 2021)We describe the idempotent Fourier multipliers that act contractively on Hp spaces of the ddimensional torus Td for d≥1 and 1≤p≤∞. When p is not an even integer, such multipliers are just restrictions of contractive ... 
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, ... 
Maximal norm Hankel operators
Brevig, Ole Fredrik; Seip, Kristian (Peer reviewed; Journal article, 2024) 
The Nehari problem for the PaleyWiener space of a disc
Brevig, Ole Fredrik; Perfekt, KarlMikael (Peer reviewed; Journal article, 2023)There is a bounded Hankel operator on the Paley–Wiener space of a disc in R2 which does not arise from a bounded symbol. 
Norm attaining vectors and Hilbert points
Brevig, Ole Fredrik; Bampouras, Konstantinos (Journal article; Peer reviewed, 2024)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) ...