Some (p, q)-Hardy type inequalities for (p, q)-integrable functions

Suriyakamol Thongjob; Kamsing Nonlaopon; Sortiris K. Ntouyas; Suriyakamol Thongjob; Kamsing Nonlaopon; Sortiris K. Ntouyas

doi:10.3934/math.2021006

AIMS Mathematics

2021, Volume 6, Issue 1: 77-89. doi: 10.3934/math.2021006

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Research article

Some (p, q)-Hardy type inequalities for (p, q)-integrable functions

1.
Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand
2.
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 Arabia

Received: 18 August 2020 Accepted: 21 September 2020 Published: 28 September 2020
MSC : 26D10, 26D15, 81P68

In this paper, we study some $(p, q)$-Hardy type inequalities for $(p, q)$-integrable functions. Moreover, we also study $(p, q)$-H?lder 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, H?lder integral inequality and Minkowski integral inequality for two variables.
- Hardy type inequalities,
- Minkowski integral inequality,
- (p, q)-calculus,
- (p, q)-integrable function
Citation: Suriyakamol Thongjob, Kamsing Nonlaopon, Sortiris K. Ntouyas. Some (p, q)-Hardy type inequalities for (p, q)-integrable functions[J]. AIMS Mathematics, 2021, 6(1): 77-89. doi: 10.3934/math.2021006

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Abstract

In this paper, we study some $(p, q)$-Hardy type inequalities for $(p, q)$-integrable functions. Moreover, we also study $(p, q)$-H?lder 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, H?lder integral inequality and Minkowski integral inequality for two variables.

References

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