Weighted Sub-Bergman Hilbert spaces in the unit ball of ℂn

Abstract

In this note, we study defect operators in the case of holomorphic functions of the unit ball of ℂn. These operators are built from weighted Bergman kernel with a holomorphic vector. We obtain a description of sub-Hilbert spaces and we give a sufficient condition so that theses spaces are the same.

Keywords

• reproducing kernel
• sub-bergman spaces
• 32a36
• 46e22