Integral means of the logarithmic derivative of Blaschke products (Q1045720)

Estimates for certain integral means for Blaschke products \[ B(z) = \prod_{n=1}^{\infty} \frac{|z_n|}{z_n} \frac{z_n - z}{1 - z_n z},\;\;\; |z_n| < 1,\;\;\; \sum_{n=1}^{\infty} (1 - |z_n|) < \infty, \] in an open unit disc are given, namely, the (Hardy) \(H_p\) integral mean \[ \int_{0}^{2\pi} \left|\frac{B^{(l)}(r e^{i \theta})}{B(r e^{i \theta})}\right|^{p} d \theta,\;\;\; l\in {\mathbb N}, \] and the (Bergman) \(A^p_{\gamma}\) integral mean \[ \int_{0}^{2\pi} \int_{0}^{1}\left|\frac{B^{(l)}(r \rho e^{i \theta})}{B(r \rho e^{i \theta})}\right|^{p} \rho (1 - \rho^2)^{\gamma} d \rho d \theta,\;\;\; l\in {\mathbb N},\; \gamma\in (-1, - \frac{l-1}{l}). \]