Author

Ole Fredrik Brevig

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Preprint Oct 2026

Extremals for linear functionals on $H^p$ are outer when $0

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 $L(f)=\|L\|$, then $f$ is an outer function. The proof is short and relies on a construction due to de Leeuw and Rudin. Our result complements work of Du...

Ole Fredrik Brevig, Øistein Søvik · 0 citations

Preprint Sep 2026

Mean values, order, and convergence in the Hardy space of Dirichlet series

Let $\mathscr{H}^2$ denote the Hilbert space of Dirichlet series with square-summable coefficients. It follows from a theorem of Bohr that if $f$ in $\mathscr{H}^2$ has a bounded analytic continuation to the right half-plane, then its norm can be computed from the mean values \[\|f\|_{\mathscr{H}^2}^2 = \lim_{\sigma\to...

Ole Fredrik Brevig, Athanasios Kouroupis · 0 citations