arXiv subjects
Publications and source records attributed to David Protas.
The relationship between the distribution of zeros of an infinite Blaschke product $B$ and the inclusion in weighted Bergman spaces $A_{\alpha}^p$ of the derivative of $B$ or the derivative of functions in its model space $H^2 \ominus BH^2$ is investigated.
Let $B$ be a Blaschke product with zeros $\{a_n\}$. If $B' \in A^p_α$ for certain $p$ and $α$, it is shown that $\sum_n (1 - |a_n|)^β < \infty$ for appropriate values of $β$. Also, if $\{a_n\}$ is uniformly discrete and if $B' \in H^p$ or $B' \in A^{1+p}$ for any $p \in (0,1)$, it is shown that $\sum_n (1 - |a_n|)^{1-p} < \infty$.