We obtain a quantitative estimate of Bergman distance when [Formula: see text] is bounded domain with log-hyperconvexity index text], as well the text]-integrability kernel text].

In this paper we consider (1) the weights of integration for which the reproducing kernel of the Bergman type can be defined, i.e., the admissible weights, and (2) the kernels defined by such weights. It is verified that the weighted Bergman kernel has the analogous properties as the classical one. We prove several sufficient conditions and necessary and sufficient conditions for a weight to be...

We apply Forelli-Rudin construction and Nakazawa’s hodograph transformation to prove a graph theoretic closed formula for invariant theoretic coefficients in the asymptotic expansion of the Szegö kernel on strictly pseudoconvex complete Reinhardt domains. The formula provides a structural analogy between the asymptotic expansion of the Bergman and Szegö kernels. It can be used to effectively co...

The reproducing kernel function of a weighted Bergman space over domains in C is known explicitly in only a small number of instances. Here, we introduce a process of orthogonal norm expansion along a subvariety of codimension 1, which also leads to a series expansion of the reproducing kernel in terms of reproducing kernels defined on the subvariety. The problem of finding the reproducing kern...

We present a method of obtaining a lower bound estimate of the curvatures of the Bergman metric without using the regularity of the kernel function on the boundary. As an application, we prove the existence of an uniform lower bound of the bisectional curvatures of the Bergman metric of a smooth bounded pseudoconvex domain near the boundary with constant Levi rank.