Carleson and vanishing Carleson measures for Besov spaces on the unit ball of CN are defined using imbeddings into Lebesgue classes via radial derivatives. The measures, some of which are infinite, are characterized in terms of Berezin transforms and Bergman-metric balls, extending results for weighted Bergman spaces. Special cases pertain to Arveson and Dirichlet spaces, and a unified view wit...

We obtain an asymptotic expansion and some regularity results for the Bergman kernel on the intersection of two balls in C.

This paper studies the boundary behavior of the Berezin transform on the C∗-algebra generated by the analytic Toeplitz operators on the Bergman space.

In the paper Gaussian curvature of Bergman metric on the unit disc and the dependence of this curvature on the weight function has been studied.

We study the relationship between the existence of nonprincipal ultrafilters over ω and the failure of the Steinhaus and Bergman properties for infinite products of finite groups.