Coorbits for projective representations with an application to Bergman spaces

Jens Gerlach Christensen, Amer H. Darweesh, Gestur Olafsson

Published 2017-04-08Version 1

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.