Abstract/Summary

Abstract: For 1≤p<∞, let Aωp be the weighted Bergman space associated with an exponential type weight ω satisfying ∫D|Kz(ξ)|ω(ξ)1/2dA(ξ)≤Cω(z)−1/2, z∈D, where Kz is the reproducing kernel of Aω2. This condition allows us to obtain some interesting reproducing kernel estimates and more estimates on the solutions of the ∂̅-equation (Theorem 2.5) for more general weight ω∗. As an application, we prove the boundedness of the Bergman projection on Lωp, identify the dual space of Aωp, and establish an atomic decomposition for it. Further, we give necessary and sufficient conditions for the boundedness and compactness of some operators acting from Aωp into Aωq, 1≤p, q<∞, such as Toeplitz and (big) Hankel operators.