In this article, we construct the canonical semipositive current or the canonical measure (= the potential of the canonical semipositive current) on a smooth projective variety of nonnegative Kodaira dimension in terms of a dynamical system of Bergman kernels. This current is considered to be a generalization of a Kähler-Einstein metric and coincides the one considered independently by J. Song ...

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...

‎In this paper we characterize Bergman spaces with‎ ‎respect to double integral of the functions $|f(z)‎ ‎-f(w)|/|z-w|$,‎ ‎$|f(z)‎ -‎f(w)|/rho(z,w)$ and $|f(z)‎ ‎-f(w)|/beta(z,w)$,‎ ‎where $rho$ and $beta$ are the pseudo-hyperbolic and hyperbolic metrics‎. ‎We prove some necessary and sufficient conditions that implies a function to be...