6 papers
A simple proof that the Riesz projection is bounded on for
Ole Fredrik Brevig
Let denote the Riesz projection on the unit circle and suppose that . We present a simple proof of the bound $\|\mathbf{P}f\|_p \leq \max(p,q)…
Harald Bohr's splitting theorem
Viktor Andersson, Ole Fredrik Brevig, Athanasios Kouroupis
We present a new elementary proof of a theorem due to Harald Bohr, which states that an unbounded, analytic, and almost periodic function in a half-plane can be written as the sum…
Contractive Hardy--Littlewood inequalities in the Dirichlet range
Ole Fredrik Brevig, Aleksei Kulikov, Kristian Seip +1
The class consists of those analytic functions in the unit disc such that \[\|f\|_{α,p}^p := |f(0)|^p+\int_0^1 \left(\frac{d}{dr} M_p^p(r,f)\right) (1-r^2)^{α-1} \,d…
Carlson's theorem and vertical limit functions
Ole Fredrik Brevig, Athanasios Kouroupis
We extend a classical theorem of Carlson on moments of Dirichlet series from to . When combined with the ergodic theorem for the Kronecker flow, a coherent…
Two footnotes to the F. & M. Riesz theorem
Ole Fredrik Brevig
We present a new proof of the F. & M. Riesz theorem on analytic measures of the unit circle that is based the following elementary inequality: If is analytic in th…
Almost periodicity and boundary values of Dirichlet series
Ole Fredrik Brevig, Athanasios Kouroupis, Karl-Mikael Perfekt
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 a…