Some classical inequalities and their applications

HUBAN M. B., GÜRDAL M., Tilki H.

Filomat, vol.35, no.7, pp.2165-2173, 2021 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 35 Issue: 7
  • Publication Date: 2021
  • Doi Number: 10.2298/fil2107165h
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.2165-2173
  • Keywords: Berezin number, Berezin symbol, Hölder-McCarthy type inequality, Quasi-paranormal operator, Reproducing kernel Hilbert space, Young type inequality
  • Isparta University of Applied Sciences Affiliated: Yes

Abstract

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