Weighted composition operators from generalized weighted Bergman spaces to weighted-type spaces.
Weighted generalization of the Ramadanov's theorem and further considerations
We study the limit behavior of weighted Bergman kernels on a sequence of domains in a complex space , and show that under some conditions on domains and weights, weighed Bergman kernels converge uniformly on compact sets. Then we give a weighted generalization of the theorem given by M. Skwarczyński (1980), highlighting some special property of the domains, on which the weighted Bergman kernels converge uniformly. Moreover, we show that convergence of weighted Bergman kernels implies this property,...