A subordination Principle. Applications

TL;DR

This paper explores a subordination principle linking properties of Hardy and Bergman spaces across different complex domains, with applications to measures, sequences, the corona theorem, and zero sets.

Contribution

It introduces a subordination principle that transfers properties from Hardy to Bergman spaces, providing new insights and applications in complex analysis.

Findings

Established a subordination principle connecting Hardy and Bergman spaces.

Applied the principle to characterize Bergman-Carleson measures and interpolating sequences.

Extended the principle to results on the Bergman-Nevanlinna class zeros.

Abstract

The subordination principle states roughly : if a property is true for Hardy spaces in some kind of domains in $C^n$ then it is also true for the Bergman spaces of the same kind of domains in $C^{n-1}$. 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.