Equivalent Statements of Two Multidimensional Hilbert-Type Integral Inequalities with Parameters

By means of the weight functions, the idea of introduced parameters and the transfer formulas, two multidimensional Hilbert-type integral inequalities with the general nonhomogeneous kernel as H(||x||αλ1||y||βλ2)(λ1,λ2≠0) are given, which are some extensions of the Hilbert-type integral inequalities...

Full description

Saved in:
Bibliographic Details
Published in:Axioms 2023-10, Vol.12 (10), p.956
Main Authors: Li, Yiyuan, Zhong, Yanru, Yang, Bicheng
Format: Article
Language:English
Subjects:
best possible constant factor
Equivalence
gamma function
Inequalities
Inequalities (Mathematics)
Inequality
Integrals
Kernels
multidimensional Hilbert-type inequality
Parameters
transfer formula
Weighting functions
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:By means of the weight functions, the idea of introduced parameters and the transfer formulas, two multidimensional Hilbert-type integral inequalities with the general nonhomogeneous kernel as H(||x||αλ1||y||βλ2)(λ1,λ2≠0) are given, which are some extensions of the Hilbert-type integral inequalities in the two-dimensional case. Some equivalent conditions of the best value and several parameters related to the new inequalities are provided. Two corollaries regarding the kernel, represented as kλ(||x||αλ1,||y||βλ2)(λ1,λ2≠0), are given, and a few new inequalities for the particular parameters are obtained.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms12100956