Bergman projection induced by kernel with integral representation

Abstract

Bounded Bergman projections $P_{\omega }:L_{\omega }^p(v)\to L_{\omega }^p(v)$, induced by reproducing kernels admitting the representation $$\frac{1}{(1-\overline{z}\zeta {)}^{\gamma }}{\int }_0^1\frac{d\nu (r)}{1-r\overline{z}\zeta },$$ and the corresponding (1,1)-inequality are characterized in terms of Bekollé-Bonami-type conditions. The two-weight inequality for the maximal Bergman projection $P_{\omega }^{+}:L_{\omega }^p(u)\to L_{\omega }^p(v)$ in terms of Sawyer-testing conditions is also discussed.

arXiv admin note: text overlap with arXiv:1304.1750 by other authors