On Hardy-type integral inequalities with the gamma function

By means of real analysis and weight functions, we obtain a few equivalent conditions of two kinds of Hardy-type integral inequalities with the non-homogeneous kernel and parameters. The constant factors related to the gamma function are proved to be the best possible. We also consider the operator...

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Detalles Bibliográficos
Autores principales: Liao, Jianquan, Yang, Bicheng
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5487938/
https://www.ncbi.nlm.nih.gov/pubmed/28680234
http://dx.doi.org/10.1186/s13660-017-1404-1
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author Liao, Jianquan
Yang, Bicheng
author_facet Liao, Jianquan
Yang, Bicheng
author_sort Liao, Jianquan
collection PubMed
description By means of real analysis and weight functions, we obtain a few equivalent conditions of two kinds of Hardy-type integral inequalities with the non-homogeneous kernel and parameters. The constant factors related to the gamma function are proved to be the best possible. We also consider the operator expressions and some cases of homogeneous kernel.
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spelling pubmed-54879382017-07-03 On Hardy-type integral inequalities with the gamma function Liao, Jianquan Yang, Bicheng J Inequal Appl Research By means of real analysis and weight functions, we obtain a few equivalent conditions of two kinds of Hardy-type integral inequalities with the non-homogeneous kernel and parameters. The constant factors related to the gamma function are proved to be the best possible. We also consider the operator expressions and some cases of homogeneous kernel. Springer International Publishing 2017-06-07 2017 /pmc/articles/PMC5487938/ /pubmed/28680234 http://dx.doi.org/10.1186/s13660-017-1404-1 Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Liao, Jianquan
Yang, Bicheng
On Hardy-type integral inequalities with the gamma function
title On Hardy-type integral inequalities with the gamma function
title_full On Hardy-type integral inequalities with the gamma function
title_fullStr On Hardy-type integral inequalities with the gamma function
title_full_unstemmed On Hardy-type integral inequalities with the gamma function
title_short On Hardy-type integral inequalities with the gamma function
title_sort on hardy-type integral inequalities with the gamma function
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5487938/
https://www.ncbi.nlm.nih.gov/pubmed/28680234
http://dx.doi.org/10.1186/s13660-017-1404-1
work_keys_str_mv AT liaojianquan onhardytypeintegralinequalitieswiththegammafunction
AT yangbicheng onhardytypeintegralinequalitieswiththegammafunction

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