On Weights Which Admit Reproducing Kernel of Szegő Type

Abstract

In this paper we generalize the concept of the Szego kernel by putting the weight of integration in the definition of the inner product in the Szego space. We give some sufficient conditions for the weight in order for the Szego kernel of the correspoding space to exist. We give examples of weights on unit ball for which there is no Szego kernel of the corresponding Szego space. Then using biholomorphisms we prove that there exist such weights for a large class of domains. At the end we show that weighted Szego kernel depends continuously in some sense on weight of integration.