Weighted Bergman Kernels Research Articles

Weighted Bergman Spaces and Carleson Measures on the Unit Ball of Cn

Let φ be a normal function on [0, 1), Bn the unit ball of Cn, and Aφp(Bn) the weighted Bergman spaces on Bn with weight φ. The purpose of this paper is to discuss some relations among Aφp(Bn), weighted Bergman kernels, and Carleson measures on Bn.

The Weighted Bergman Projection and Related Theory on the Minimal Ball

In this note we compute the weighted Bergman kernel of the unit ball with respect to the smallest norm in C n that extends the euclidian norm in R n . We establish the regularity properties of the corresponding weighted Bergman projection and give some applications.

On weighted Bergman kernels of bounded domains

On weighted Bergman kernels of bounded domains

On weights which admit the reproducing kernel of Bergman type

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 an admissible weight. We give also an example of a weight which is not of this class. As a positive example we consider the weight μ(z) = (Imz)2 defined on the unit disk in ℂ.