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

Abstract

Let $C(k,p)$ denote the smallest real number such that the estimate $|a_k|\le C(k,p)\Vert f{\Vert }_{H^p}$ holds for every $f(z)={\sum }_{n\ge 0}{a}_n{z}^n$ 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.

Minor corrections. This paper has been has been accepted for publication in Proceedings of the AMS