Abstract

In this paper, we consider estimates with loss for the Bergman projections of bounded symmetric domains of n in their Harish-Chandra realizations. This paper is twofold: on one side we develop transfer methods between these bounded domains and their Cayley transform; on the other side we give a new range of q such that the Bergman projection is bounded from L(n) to Lq(n) where n is the Lie ball of n.