Bergman Projection and Bergman Spaces

摘要

In this paper we study mapping properties of the Bergman projection P, i.e. which function spaces or classes are preserved by P. It is shown that the Bergman projection is of weak type (1, 1) and bounded on the Orlicz space L~ψ(D, dA) iff L~ψ(D, dA) is reflexive. So the dual space of the Bergman space L_a~ψ is L~ψ if L~ψ (D, dA) is reflexive, where ψ and ψ are a pair of complementary Young functions. In addition, we also get that the Kolmogorov type inequality and the Zygmund type inequality hold for the Bergman projection.