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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
Citation: 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

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

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