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arXiv · 1905.09547

Coefficient estimates for $H^p$ spaces with $0<p<1$

Ole Fredrik Brevig·Eero Saksman
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Abstract

Let $C(k,p)$ denote the smallest real number such that the estimate $|a_k|\leq C(k,p)\|f\|_{H^p}$ holds for every $f(z)=\sum_{n\geq0}a_n z^n$ in the $H^p$ space of the unit disc. We compute $C(2,p)$ for $0<p<1$ and $C(3,2/3)$, and identify the functions attaining equality in the estimate.

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Ole Fredrik Brevig, Eero Saksman. 2019-05-23. Coefficient estimates for $H^p$ spaces with $0<p<1$. https://doi.org/10.1090/proc%2F14995

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