The Equivalent Conditions for a Second Kind of Hardy-Type Inequality Related to Gamma Function

ZHONG Jianhua; ZENG Zhihong; CHEN yanqing; CHEN Qiang

doi:10.6054/j.jscnun.2020050

Journal of South China Normal University (Natural Science Edition) > 2020 > 52(3): 101-105. > DOI: 10.6054/j.jscnun.2020050

ZHONG Jianhua, ZENG Zhihong, CHEN yanqing, CHEN Qiang. The Equivalent Conditions for a Second Kind of Hardy-Type Inequality Related to Gamma Function[J]. Journal of South China Normal University (Natural Science Edition), 2020, 52(3): 101-105. DOI: 10.6054/j.jscnun.2020050

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The Equivalent Conditions for a Second Kind of Hardy-Type Inequality Related to Gamma Function

1.
Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China
2.
Editorial Department of the University Journal, Guangdong University of Education, Guangzhou 510303, China
3.
Guangzhou Jude Middle School, Guangzhou 510305, China
4.
Department of Computer Science, Guangdong University of Education, Guangzhou 510303, China

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Received Date: September 24, 2019
Available Online: March 21, 2021

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Abstract

Abstract

Two lemmas that are related to the estimate of weight function and the proving of best constant are obtained with the introduction of suitable parameters and the use of the way and techniques of real analysis and weight functions. On this basis, a few equivalent conditions for a second kind of Hardy-type integral inequality with a non-homogeneous kernel, related to a parameter and a best constant factor expressed in terms of Gamma function, are built. Meanwhile, some equivalent conditions for a second kind of Hardy-type integral inequality with the homogeneous kernel are deduced.
- Hardy-type integral inequality,
- weight function,
- equivalent form,
- Gamma function

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