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arXiv · 2011.07790

F. Wiener's trick and an extremal problem for $H^p$

Ole Fredrik Brevig·Sigrid Grepstad·Sarah May Instanes
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Abstract

For $0<p \leq \infty$, let $H^p$ denote the classical Hardy space of the unit disc. We consider the extremal problem of maximizing the modulus of the $k$th Taylor coefficient of a function $f \in H^p$ which satisfies $\|f\|_{H^p}\leq1$ and $f(0)=t$ for some $0 \leq t \leq 1$. In particular, we provide a complete solution to this problem for $k=1$ and $0<p<1$. We also study F. Wiener's trick, which plays a crucial role in various coefficient-related extremal problems for Hardy spaces.

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Ole Fredrik Brevig, Sigrid Grepstad, Sarah May Instanes. 2020-11-16. F. Wiener's trick and an extremal problem for $H^p$. https://doi.org/10.1007/s40315-022-00469-x

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