Atomic decompositions of mixed norm Bergman spaces on tube type domains

TL;DR

This paper develops new atomic decompositions for mixed norm Bergman spaces on tube type domains, extending previous work on Besov spaces and offering a broader applicability than classical methods.

Contribution

It introduces novel atomic decompositions for Bergman spaces on tube type domains, expanding the range of spaces covered compared to classical approaches.

Findings

New atomic decompositions for Bergman spaces on tube type domains.

Extension of atomic decomposition methods to a larger class of Bergman spaces.

Alternative approach to classical results by Coifman and Rochberg.

Abstract

We use the author's previous work on atomic decompositions of Besov spaces with spectrum on symmetric cones, to derive new atomic decompositions for Bergman spaces on tube type domains. It is related to work by Ricci and Taibleson who derived decompositions for classical Besov spaces from atomic decompositions of Bergman spaces on the upper half plane. Moreover, for this class of domains our method is an alternative to classical results by Coifman and Rochberg, and it works for a larger range of Bergman spaces.