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

Abstract

For $0<p\le \infty$, 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 $\Vert f{\Vert }_{H^p}\le 1$ and $f(0)=t$ for some $0\le t\le 1$. 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.

This paper has been accepted for publication in Computational Methods and Function Theory

References in corpus (2)

• The Krzyż conjecture revisited
• Coefficient estimates for $H^p$ spaces with $0<p<1$