-Estimates of the Bergman projection in the Lie ball of

In this paper, we consider estimates with loss for the Bergman projections of bounded symmetric domains of ℂn 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∞(ℬn) to Lq(ℬn) where ℬn is the Lie ball of ℂn.