论文标题
F. Wiener的技巧和$ H^p $的极端问题
F. Wiener's trick and an extremal problem for $H^p$
论文作者
论文摘要
对于$ 0 <p \ leq \ infty $，令$ h^p $表示单位光盘的经典耐寒空间。我们考虑了最大化H^p $ $ k $ th taylor系数的极端问题，它满足了$ \ | f \ | _ {h^p} \ leq1 $ and $ f（0）= t $ for Leq t \ leq t \ leq leq 1 $。特别是，我们为$ k = 1 $和$ 0 <p <1 $提供了一个完整的解决方案。我们还研究了维纳（F. Wiener）的技巧，该技巧在与系数相关的极端问题中起着至关重要的作用。
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.
