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...

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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
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Yang, Bicheng
description 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.
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subjects best possible constant factor
Equivalence
gamma function
Inequalities
Inequalities (Mathematics)
Inequality
Integrals
Kernels
multidimensional Hilbert-type inequality
Parameters
transfer formula
Weighting functions
title Equivalent Statements of Two Multidimensional Hilbert-Type Integral Inequalities with Parameters
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