On the boundedness of Bergman projection

Abstract

The main purpose of this survey is to gather results on the boundedness of the Bergman projection. First, we shall go over some equivalent norms on weighted Bergman spaces $A_{\omega }^p$ which are useful in the study of this question. In particular, we shall focus on a decomposition norm theorem for radial weights~$\omega$ with the doubling property ${\int }_r^1\omega (s)ds\le C{\int }_{\frac{1+r}{2}}^1\omega (s)ds$.

This paper is related to the minicourse "Decomposition norm theorem, L^p-behavior of reproducing kernels and two weight inequality for Bergman projection", the first author delivered in the meeting "VI International Course of Mathematical Analysis in Andalucía (VI CIDAMA)" celebrated at Antequera (Spain), September 2014