An extended Hilbert’s integral inequality in the whole plane with parameters

Abstract By introducing independent parameters and interval variables, applying the weight functions and the technique of real analysis, an extended Hilbert’s integral inequality in the whole plane with parameters and a best possible constant factor is provided. The equivalent forms, the reverses, a...

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Main Authors:	Leping He, Yin Li, Bicheng Yang
Format:	Article
Language:	English
Published:	SpringerOpen 2018-08-01
Series:	Journal of Inequalities and Applications
Subjects:	Hilbert’s integral inequality Weight function Equivalent form Operator Norm
Online Access:	http://link.springer.com/article/10.1186/s13660-018-1810-z

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spelling	doaj-ca1405f77b764842a7847e10c3c746012020-11-24T21:16:19ZengSpringerOpenJournal of Inequalities and Applications1029-242X2018-08-012018111110.1186/s13660-018-1810-zAn extended Hilbert’s integral inequality in the whole plane with parametersLeping He0Yin Li1Bicheng Yang2College of Mathematics and Statistics, Jishou UniversityCollege of Mathematics and Statistics, Jishou UniversityDepartment of Mathematics, Guangdong University of EducationAbstract By introducing independent parameters and interval variables, applying the weight functions and the technique of real analysis, an extended Hilbert’s integral inequality in the whole plane with parameters and a best possible constant factor is provided. The equivalent forms, the reverses, and the related homogeneous forms with particular parameters are considered. Meanwhile, an extended Hilbert’s integral operator in the whole plane is defined, and the operator expressions for the equivalent inequalities are obtained.http://link.springer.com/article/10.1186/s13660-018-1810-zHilbert’s integral inequalityWeight functionEquivalent formOperatorNorm
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Leping He Yin Li Bicheng Yang
spellingShingle	Leping He Yin Li Bicheng Yang An extended Hilbert’s integral inequality in the whole plane with parameters Journal of Inequalities and Applications Hilbert’s integral inequality Weight function Equivalent form Operator Norm
author_facet	Leping He Yin Li Bicheng Yang
author_sort	Leping He
title	An extended Hilbert’s integral inequality in the whole plane with parameters
title_short	An extended Hilbert’s integral inequality in the whole plane with parameters
title_full	An extended Hilbert’s integral inequality in the whole plane with parameters
title_fullStr	An extended Hilbert’s integral inequality in the whole plane with parameters
title_full_unstemmed	An extended Hilbert’s integral inequality in the whole plane with parameters
title_sort	extended hilbert’s integral inequality in the whole plane with parameters
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1029-242X
publishDate	2018-08-01
description	Abstract By introducing independent parameters and interval variables, applying the weight functions and the technique of real analysis, an extended Hilbert’s integral inequality in the whole plane with parameters and a best possible constant factor is provided. The equivalent forms, the reverses, and the related homogeneous forms with particular parameters are considered. Meanwhile, an extended Hilbert’s integral operator in the whole plane is defined, and the operator expressions for the equivalent inequalities are obtained.
topic	Hilbert’s integral inequality Weight function Equivalent form Operator Norm
url	http://link.springer.com/article/10.1186/s13660-018-1810-z
work_keys_str_mv	AT lepinghe anextendedhilbertsintegralinequalityinthewholeplanewithparameters AT yinli anextendedhilbertsintegralinequalityinthewholeplanewithparameters AT bichengyang anextendedhilbertsintegralinequalityinthewholeplanewithparameters AT lepinghe extendedhilbertsintegralinequalityinthewholeplanewithparameters AT yinli extendedhilbertsintegralinequalityinthewholeplanewithparameters AT bichengyang extendedhilbertsintegralinequalityinthewholeplanewithparameters
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An extended Hilbert’s integral inequality in the whole plane with parameters

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