Positive kernel functions and Bergman spaces (Q1112214)

Using the positive (``Poisson-like'') reproducing kernel for the weighted Bergman spaces \(A^{p,\delta}({\mathbb{B}})\), the author obtains Hardy- Littlewood inequalities for functions in these spaces. Similar results are obtained in the setting of the generalized half plane in \({\mathbb{C}}^ n\). As an application, the author treats the Mackey topology on \(A^{p,\delta}({\mathbb{B}})\), \(0<p<1\) and extends a one variable result due to \textit{J. Shapiro} [Duke Math. J. 43, 187-202 (1976; Zbl 0354.46036)].