On the Norm of a Multidimensional Hilbert-Type Operator

In this paper we consider multidimensional Hilbert-type integral inequalities with non-conjugate exponents and homogeneous kernels of negative degree. As an application, we define related Hilbert-type integral operators and consider their norms. The problem of determining the norm of such operators...

Full description

Saved in:
Bibliographic Details
Published inSarajevo journal of mathematics Vol. 7; no. 2; pp. 223 - 243
Main Authors Bicheng, Yang, Krnić, Mario
Format Journal Article
LanguageEnglish
Published 10.06.2024
Online AccessGet full text

Cover

More Information
Summary:In this paper we consider multidimensional Hilbert-type integral inequalities with non-conjugate exponents and homogeneous kernels of negative degree. As an application, we define related Hilbert-type integral operators and consider their norms. The problem of determining the norm of such operators is equivalent to the problem of the best possible constant factors involved in the right-hand sides of related inequalities. In such a way, we obtain the norms and the best possible constant factors in some general settings with conjugate exponents. In particular, we obtain generalizations of some recent results from the literature.   2000 Mathematics Subject Classification. Primary 47A07, 26D15
ISSN:1840-0655
2233-1964
DOI:10.5644/SJM.07.2.08