Equivalent Statements of Two Multidimensional Hilbert-Type Integral Inequalities with Parameters-Reference-Cited by-同舟云学术

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

Published:2023-10-10 Issue:10 Volume:12 Page:956
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Li Yiyuan¹,Zhong Yanru²,Yang Bicheng³

Affiliation:

1. School of Art and Design, Guilin University of Electronic Technology, Guilin 541004, China

2. School of Computer Science and Information Security, Guilin University of Electronic Technology, Guilin 541004, China

3. School of Mathematics, Guangdong University of Education, Guangzhou 510303, China

Abstract

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.

Funder

National Natural Science Foundation of China

Innovation Key Project of Guangxi Province

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/10/956/pdf

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