Some (<em>p, q</em>)-Hardy type inequalities for (<em>p, q</em>)-integrable functions

In this paper, we study some $(p,q)$-Hardy type inequalities for $(p,q)$-integrable functions. Moreover, we also study $(p,q)$-Hölder integral inequality and $(p,q)$-Minkowski integral inequality for two variables. By taking $p=1$ and $q\to 1$, our results reduce to classical results on Hardy type i...

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Main Authors:	Suriyakamol Thongjob, Kamsing Nonlaopon, Sortiris K. Ntouyas
Format:	Article
Language:	English
Published:	AIMS Press 2021-10-01
Series:	AIMS Mathematics
Subjects:	hardy type inequalities minkowski integral inequality (<i>p q</i>)-calculus q</i>)-integrable function
Online Access:	https://www.aimspress.com/article/10.3934/math.2021006/fulltext.html

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spelling	doaj-735f97d1ff304649a3c59762465457d02020-11-25T03:34:50ZengAIMS PressAIMS Mathematics2473-69882021-10-0161778910.3934/math.2021006Some (<em>p, q</em>)-Hardy type inequalities for (<em>p, q</em>)-integrable functionsSuriyakamol Thongjob0Kamsing Nonlaopon1Sortiris K. Ntouyas21 Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand1 Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand2 Department of Mathematics, University of Ioannina, Ioannina 45110, Greece 3 Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaIn this paper, we study some $(p,q)$-Hardy type inequalities for $(p,q)$-integrable functions. Moreover, we also study $(p,q)$-Hölder integral inequality and $(p,q)$-Minkowski integral inequality for two variables. By taking $p=1$ and $q\to 1$, our results reduce to classical results on Hardy type inequalities, Hölder integral inequality and Minkowski integral inequality for two variables.https://www.aimspress.com/article/10.3934/math.2021006/fulltext.htmlhardy type inequalitiesminkowski integral inequality(<i>pq</i>)-calculusq</i>)-integrable function
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Suriyakamol Thongjob Kamsing Nonlaopon Sortiris K. Ntouyas
spellingShingle	Suriyakamol Thongjob Kamsing Nonlaopon Sortiris K. Ntouyas Some (<em>p, q</em>)-Hardy type inequalities for (<em>p, q</em>)-integrable functions AIMS Mathematics hardy type inequalities minkowski integral inequality (<i>p q</i>)-calculus q</i>)-integrable function
author_facet	Suriyakamol Thongjob Kamsing Nonlaopon Sortiris K. Ntouyas
author_sort	Suriyakamol Thongjob
title	Some (<em>p, q</em>)-Hardy type inequalities for (<em>p, q</em>)-integrable functions
title_short	Some (<em>p, q</em>)-Hardy type inequalities for (<em>p, q</em>)-integrable functions
title_full	Some (<em>p, q</em>)-Hardy type inequalities for (<em>p, q</em>)-integrable functions
title_fullStr	Some (<em>p, q</em>)-Hardy type inequalities for (<em>p, q</em>)-integrable functions
title_full_unstemmed	Some (<em>p, q</em>)-Hardy type inequalities for (<em>p, q</em>)-integrable functions
title_sort	some (<em>p, q</em>)-hardy type inequalities for (<em>p, q</em>)-integrable functions
publisher	AIMS Press
series	AIMS Mathematics
issn	2473-6988
publishDate	2021-10-01
description	In this paper, we study some $(p,q)$-Hardy type inequalities for $(p,q)$-integrable functions. Moreover, we also study $(p,q)$-Hölder integral inequality and $(p,q)$-Minkowski integral inequality for two variables. By taking $p=1$ and $q\to 1$, our results reduce to classical results on Hardy type inequalities, Hölder integral inequality and Minkowski integral inequality for two variables.
topic	hardy type inequalities minkowski integral inequality (<i>p q</i>)-calculus q</i>)-integrable function
url	https://www.aimspress.com/article/10.3934/math.2021006/fulltext.html
work_keys_str_mv	AT suriyakamolthongjob someempqemhardytypeinequalitiesforempqemintegrablefunctions AT kamsingnonlaopon someempqemhardytypeinequalitiesforempqemintegrablefunctions AT sortiriskntouyas someempqemhardytypeinequalitiesforempqemintegrablefunctions
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Some (<em>p, q</em>)-Hardy type inequalities for (<em>p, q</em>)-integrable functions

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