Ole Fredrik Brevig

activity

20132026

most citedThe multiplicative Hilbert matrix

57 citations · 299 across the 47 of their papers we have counts for

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32 papers · 1 filter

math.FA2026

Extremals for linear functionals on $H^{p}$ are outer when $0 < p < 1$

Ole Fredrik Brevig, Øistein Søvik

Let $L$ be a nontrivial bounded linear functional on the Hardy space $H^{p}$ of the unit disc. We prove that if $0 < p < 1$ and if $f$ in the unit sphere of $H^{p}$ satisfies $L (f) = ∥ L ∥$ ,…

math.FA2026

Contractivity of Rudin's diagonal restriction operator for $H^{p}$ of the polydisc

Ole Fredrik Brevig, Javier Gómez-Serrano, Joaquim Ortega-Cerdà +1

We establish that Rudin's diagonal restriction operator is contractive from the Hardy space $H^{p}$ of the bidisc to the Bergman space $A^{p}$ of the disc for $2 \leq p < \infty$ , and cha…

math.FA2026

Bohr sets for multiplier algebras of complete Pick spaces

Ole Fredrik Brevig, Kristian Seip, Ilya Zlotnikov

We reexamine F. Wiener's classical proof that the Bohr radius of $H^{\infty}$ is $1/3$ . We replace $H^{\infty}$ by the multiplier algebras of complete Pick spaces and describe the Bohr…

math.FA2024

Critical exponents of the Riesz projection

Ole Fredrik Brevig, Adrián Llinares, Kristian Seip

Let $p_{d} (q)$ denote the critical exponent of the Riesz projection from $L^{q} (T^{d})$ to the Hardy space $H^{p} (T^{d})$ , where $T$ is the unit circle.…

math.FA2023

Norm attaining vectors and Hilbert points

Konstantinos Bampouras, Ole Fredrik Brevig

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…

math.FA2023

The norm of the backward shift on $H^{1}$ is $\frac{2}{3}$

Ole Fredrik Brevig, Kristian Seip

We show that the norm of the backward shift operator on $H^{1}$ is $2/ 3$ , and we identify the functions for which the norm is attained.

math.FA2023★ 1 cited

Maximal norm Hankel operators

Ole Fredrik Brevig, Kristian Seip

A Hankel operator $H_{φ}$ on the Hardy space $H^{2}$ of the unit circle with analytic symbol $φ$ has minimal norm if $∥ H_{φ} ∥ = ∥ φ ∥_{2}$ and maximal norm if $\|\mathbf{…

math.FA2022★ 2 cited

Correction to: Weak product spaces of Dirichlet series

Ole Fredrik Brevig, Karl-Mikael Perfekt

We correct the proof of Theorem~8 in [\emph{Weak product spaces of Dirichlet series}, Integral Equations Operator Theory \textbf{86} (2016), no.~4, 453--473.]

math.FA2022★ 2 cited

The Nehari problem for the Paley--Wiener space of a disc

Ole Fredrik Brevig, Karl-Mikael Perfekt

There is a bounded Hankel operator on the Paley--Wiener space of a disc in $R^{2}$ which does not arise from a bounded symbol.

math.FA2022★ 2 cited

Hilbert points in Hilbert space-valued $L^{p}$ spaces

Ole Fredrik Brevig, Sigrid Grepstad

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 $∥ φ ∥_{p} \leq ∥ φ + f ∥_{p}$ whenever $\la…

math.FA2021★ 2 cited

Orthogonal decomposition of composition operators on the $H^{2}$ space of Dirichlet series

Ole Fredrik Brevig, Karl-Mikael Perfekt

Let $H^{2}$ denote the Hilbert space of Dirichlet series with square-summable coefficients. We study composition operators $C_{φ}$ on $H^{2}$ which are gene…

math.FA2021

Minimal norm Hankel operators

Ole Fredrik Brevig

Let $φ$ be a function in the Hardy space $H^{2} (T^{d})$ . The associated (small) Hankel operator $H_{φ}$ is said to have minimal norm if the general lower norm bound $\|…

math.FA2021★ 3 cited

Hilbert points in Hardy spaces

Ole Fredrik Brevig, Joaquim Ortega-Cerdà, Kristian Seip

A Hilbert point in $H^{p} (T^{d})$ , for $d \geq 1$ and $1 \leq p \leq \infty$ , is a nontrivial function $φ$ in $H^{p} (T^{d})$ such that $\| φ\|_{H^p(\mathbb{T}^d)} \leq \|φ+…

math.FA2021★ 3 cited

Idempotent Fourier multipliers acting contractively on $H^{p}$ spaces

Ole Fredrik Brevig, Joaquim Ortega-Cerdà, Kristian Seip

We describe the idempotent Fourier multipliers that act contractively on $H^{p}$ spaces of the $d$ -dimensional torus $T^{d}$ for $d \geq 1$ and $1 \leq p \leq \infty$ . When $p$ …

math.FA2020★ 17 cited

A mean counting function for Dirichlet series and compact composition operators

Ole Fredrik Brevig, Karl-Mikael Perfekt

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…

math.FA2020★ 4 cited

The spectrum of some Hardy kernel matrices

Ole Fredrik Brevig, Karl-Mikael Perfekt, Alexander Pushnitski

For $α > 0$ we consider the operator $K_{α} : ℓ^{2} \to ℓ^{2}$ corresponding to the matrix \[\left(\frac{(nm)^{-\frac{1}{2}+α}}{[\max(n,m)]^{2α}}\right)_{n,m=1}^\infty.\] By int…

math.FA2019★ 1 cited

Projecting onto Helson matrices in Schatten classes

Ole Fredrik Brevig, Nazar Miheisi

A Helson matrix is an infinite matrix $A = (a_{m, n})_{m, n \geq 1}$ such that the entry $a_{m, n}$ depends only on the product $mn$ . We demonstrate that the orthogonal projection from…

math.FA2019★ 1 cited

Coefficient estimates for $H^{p}$ spaces with $0 < p < 1$

Ole Fredrik Brevig, Eero Saksman

Let $C (k, p)$ denote the smallest real number such that the estimate $∣ a_{k} ∣ \leq C (k, p) ∥ f ∥_{H^{p}}$ holds for every $f (z) = \sum_{n \geq 0} a_{n} z^{n}$ in the $H^{p}$ space of the unit disc. W…

math.FA2019★ 10 cited

Norms of composition operators on the $H^{2}$ space of Dirichlet series

Ole Fredrik Brevig, Karl-Mikael Perfekt

We consider composition operators $C_{φ}$ on the Hardy space of Dirichlet series $H^{2}$ , generated by Dirichlet series symbols $φ$ . We prove two different subordin…

math.FA2018★ 3 cited

Linear functions and duality on the infinite polytorus

Ole Fredrik Brevig

We consider the following question: Are there exponents $2 < p < q$ such that the Riesz projection is bounded from $L^{q}$ to $L^{p}$ on the infinite polytorus? We are unable to answer the…

math.FA2018★ 18 cited

Linear space properties of $H^{p}$ spaces of Dirichlet series

Andriy Bondarenko, Ole Fredrik Brevig, Eero Saksman +1

We study $H^{p}$ spaces of Dirichlet series, called $H^{p}$ , for the range $0 < p < \infty$ . We begin by showing that two natural ways to define $H^{p}$ coincide. We the…

math.FA2017★ 13 cited

Contractive inequalities for Hardy spaces

Ole Fredrik Brevig, Joaquim Ortega-Cerdà, Kristian Seip +1

We state and discuss several interrelated results, conjectures, and questions regarding contractive inequalities for classical $H^{p}$ spaces of the unit disc. We study both coeffici…

math.FA2017★ 17 cited

Sharp norm estimates for composition operators and Hilbert-type inequalities

Ole Fredrik Brevig

Let $H^{2}$ denote the Hardy space of Dirichlet series $f (s) = \sum_{n \geq 1} a_{n} n^{- s}$ with square summable coefficients and suppose that $φ$ is a symbol generating a com…

math.FA2017★ 14 cited

Contractive inequalities for Bergman spaces and multiplicative Hankel forms

Frédéric Bayart, Ole Fredrik Brevig, Antti Haimi +2

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 i…

Extremals for linear functionals on Hp are outer when 0<p<1

Contractivity of Rudin's diagonal restriction operator for Hp of the polydisc

Bohr sets for multiplier algebras of complete Pick spaces

Critical exponents of the Riesz projection

Norm attaining vectors and Hilbert points

The norm of the backward shift on H1 is 3​2​

Maximal norm Hankel operators

Correction to: Weak product spaces of Dirichlet series

The Nehari problem for the Paley--Wiener space of a disc

Hilbert points in Hilbert space-valued Lp spaces

Orthogonal decomposition of composition operators on the H2 space of Dirichlet series

Minimal norm Hankel operators

Hilbert points in Hardy spaces

Idempotent Fourier multipliers acting contractively on Hp spaces

A mean counting function for Dirichlet series and compact composition operators

The spectrum of some Hardy kernel matrices

Projecting onto Helson matrices in Schatten classes

Coefficient estimates for Hp spaces with 0<p<1

Norms of composition operators on the H2 space of Dirichlet series

Linear functions and duality on the infinite polytorus

Linear space properties of Hp spaces of Dirichlet series

Contractive inequalities for Hardy spaces

Sharp norm estimates for composition operators and Hilbert-type inequalities

Contractive inequalities for Bergman spaces and multiplicative Hankel forms

Extremals for linear functionals on $H^{p}$ are outer when $0 < p < 1$

Contractivity of Rudin's diagonal restriction operator for $H^{p}$ of the polydisc

The norm of the backward shift on $H^{1}$ is $\frac{2}{3}$

Hilbert points in Hilbert space-valued $L^{p}$ spaces

Orthogonal decomposition of composition operators on the $H^{2}$ space of Dirichlet series

Idempotent Fourier multipliers acting contractively on $H^{p}$ spaces

Coefficient estimates for $H^{p}$ spaces with $0 < p < 1$

Norms of composition operators on the $H^{2}$ space of Dirichlet series

Linear space properties of $H^{p}$ spaces of Dirichlet series