Bergman Spaces Over The Siegel Upper Half-space

In this thesis we prove that, when1<p<∞, the Bergman projection P on Un extends to a bounded linear operator from LP to AP. Then, we obtain the main result in this thesis:The dual space of Bergman spaces AP(Un)(1<p<∞) is simply Aq(Un), where q=p/p-1. Besides, we prove that when1<p<∞, the Berezin transform Bun extends to a bounded linear operator from Lp to LP.