Blaschke products with derivative in function spaces

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