Blaschke products with derivative in function spaces

Abstract

Let $B$ be a Blaschke product with zeros $\{a_n\}$. If $B^{\prime }\in A_{\alpha }^p$ for certain $p$ and $\alpha$, it is shown that ${\sum }_n(1-|a_n|{)}^{\beta }<\infty$ for appropriate values of $\beta$. Also, if $\{a_n\}$ is uniformly discrete and if $B^{\prime }\in H^p$ or $B^{\prime }\in A^{1+p}$ for any $p\in (0,1)$, it is shown that ${\sum }_n(1-|a_n|{)}^{1-p}<\infty$.

arXiv commentClarified a few points. Accepted for publication in the Kodai Mathematical Journal

References in corpus (1)

• On Blaschke products with derivatives in Bergman spaces with normal weights