Boundedness of the Bergman type operators on mixed norm spaces

Abstract

Conditions sufficient for boundedness of the Bergman type operators on certain mixed norm spaces $L_{p,q}(\varphi )\ (0<p<1, 1<q<\infty )$ of functions on the unit ball of $C^n$ are given, and this is used to solve Gleason’s problem for the mixed norm spaces $H_{p,q}(\varphi )\ (0<p<1,1<q<\infty )$.