# Atomic decomposition and interpolation via the complex method for mixed norm Bergman spaces on tube domains over symmetric cones

## TL;DR

This paper develops atomic decomposition and interpolation characterizations for mixed norm weighted Bergman spaces on tube domains over symmetric cones, using a Whitney decomposition and complex interpolation methods.

## Contribution

It introduces an atomic decomposition theorem and characterizes interpolation spaces for mixed norm weighted Bergman spaces on symmetric cone tube domains.

## Key findings

- Atomic decomposition theorem established for these spaces.
- Interpolation spaces characterized via the complex method.
- Provides tools for analysis on symmetric cone tube domains.

## Abstract

Starting from an adapted Whitney decomposition of tube domains in $\C^n$ over irreducible symmetric cones of $\R^n,$ we prove an atomic decomposition theorem in mixed norm weighted Bergman spaces on these domains. We also characterize the interpolation space via the complex method between two mixed norm weighted Bergman spaces.