A subordination principle. Applications

Abstract

This subordination principle states roughly: if a property is true for Hardy spaces in some kind of domains in \({\mathbb{C}}^{n}\) then it is also true for the Bergman spaces of the same kind of domains in \({\mathbb{C}}^{n-1}.\) We give applications of this principle to Bergman-Carleson measures, interpolating sequences for Bergman spaces, \(A^{p}\) Corona theorem and characterization of the zeros set of Bergman-Nevanlinna class. These applications give precise results for bounded strictly-pseudo convex domains and bounded convex domains of finite type in \({\mathbb{C}}^{n}.\)