Some classical inequalities and their applications

Abstract

In this paper, we define analogies of classical Hölder-McCarthy and Young type inequalities in terms of Berezin symbols of operators on a reproducing kernel Hilbert space H=H(Ω). These inequalities are applied in proving some new inequalities for Berezin number of operators. We also define quasi-paranormal and absolute-k-quasi paranormal operators and study their properties by using Berezin symbols.