Parameterized Hilbert-Type Integral Inequalities in the Whole Plane

By the use of the way of real analysis, we estimate the weight functions and give some new Hilbert-type integral inequalities in the whole plane with nonhomogeneous kernels and multiparameters. The constant factors related to the hypergeometric function and the beta function are proved to be the bes...

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Detalles Bibliográficos
Autores principales: Huang, Qiliang, Wu, Shanhe, Yang, Bicheng
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4152985/
https://www.ncbi.nlm.nih.gov/pubmed/25215314
http://dx.doi.org/10.1155/2014/169061
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author Huang, Qiliang
Wu, Shanhe
Yang, Bicheng
author_facet Huang, Qiliang
Wu, Shanhe
Yang, Bicheng
author_sort Huang, Qiliang
collection PubMed
description By the use of the way of real analysis, we estimate the weight functions and give some new Hilbert-type integral inequalities in the whole plane with nonhomogeneous kernels and multiparameters. The constant factors related to the hypergeometric function and the beta function are proved to be the best possible. We also consider the equivalent forms, the reverses, and some particular cases in the homogeneous kernels.
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spelling pubmed-41529852014-09-11 Parameterized Hilbert-Type Integral Inequalities in the Whole Plane Huang, Qiliang Wu, Shanhe Yang, Bicheng ScientificWorldJournal Research Article By the use of the way of real analysis, we estimate the weight functions and give some new Hilbert-type integral inequalities in the whole plane with nonhomogeneous kernels and multiparameters. The constant factors related to the hypergeometric function and the beta function are proved to be the best possible. We also consider the equivalent forms, the reverses, and some particular cases in the homogeneous kernels. Hindawi Publishing Corporation 2014 2014-08-19 /pmc/articles/PMC4152985/ /pubmed/25215314 http://dx.doi.org/10.1155/2014/169061 Text en Copyright © 2014 Qiliang Huang et al. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Huang, Qiliang
Wu, Shanhe
Yang, Bicheng
Parameterized Hilbert-Type Integral Inequalities in the Whole Plane
title Parameterized Hilbert-Type Integral Inequalities in the Whole Plane
title_full Parameterized Hilbert-Type Integral Inequalities in the Whole Plane
title_fullStr Parameterized Hilbert-Type Integral Inequalities in the Whole Plane
title_full_unstemmed Parameterized Hilbert-Type Integral Inequalities in the Whole Plane
title_short Parameterized Hilbert-Type Integral Inequalities in the Whole Plane
title_sort parameterized hilbert-type integral inequalities in the whole plane
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4152985/
https://www.ncbi.nlm.nih.gov/pubmed/25215314
http://dx.doi.org/10.1155/2014/169061
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AT wushanhe parameterizedhilberttypeintegralinequalitiesinthewholeplane
AT yangbicheng parameterizedhilberttypeintegralinequalitiesinthewholeplane

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