HARDY-HILBERT'S INEQUALITY AND POWER INEQUALITIES FOR BEREZIN NUMBERS OF OPERATORS
MATHEMATICAL INEQUALITIES & APPLICATIONS, vol.19, no.3, pp.883-891, 2016 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 19 Issue: 3
- Publication Date: 2016
- Doi Number: 10.7153/mia-19-64
- Journal Name: MATHEMATICAL INEQUALITIES & APPLICATIONS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.883-891
- Keywords: Hardy inequality, Hardy-Hilbert inequality, Berezin symbol, Berezin number, positive operator, self-adjoint operator, REPRODUCING KERNELS, SPACES, SYMBOL
- Süleyman Demirel University Affiliated: Yes
Abstract
We give operator analogues of some classical inequalities, including Hardy and Hardy-Hilbert type inequalities for numbers. We apply these operator forms of such inequalities for proving some power inequalities for the so-called Berezin number of self-adjoint and positive operators acting on Reproducing Kernel Hilbert Spaces (RKHSs). More precisely, we prove that