# Coorbits for projective representations with an application to Bergman spaces

## TL;DR

This paper extends representation theory techniques to projective representations, enabling atomic decompositions of Bergman spaces on the unit ball via the holomorphic discrete series.

## Contribution

It introduces methods for atomic decompositions using projective representations, expanding the scope of classical Banach space analysis.

## Key findings

- Atomic decompositions of Bergman spaces achieved
- Extended techniques to include projective representations
- Applied to holomorphic discrete series for isometry groups

## Abstract

Recently representation theory has been used to provide atomic decompositions for a large collection of classical Banach spaces. In this paper we extend the techniques to also include projective representations. As our main application we obtain atomic decompositions of Bergman spaces on the unit ball through the holomorphic discrete series for the group of isometries of the ball.