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Research Article | Open Access

Hardy type identities and inequalities with divergence type operators on smooth metric measure spaces

Pengyan Wang, Jiahao Wang( )
School of Mathematics and Statistics, Xinyang Normal University, Xinyang, 464000, China
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Abstract

We gave the Hardy type identities and inequalities for the divergence type operator L f , V on smooth metric measure spaces. Additionally, we improved a Rellich type inequality by using the improved Hardy type inequality. Our results improved and included many previously known results as special cases.

Keywords

Hardy type inequalityHardy type identitysmooth metric measure spacedivergence type operator
CLC number: 53C21, 26D10

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AIMS Mathematics
Volume 9 Issue 6,
May 2024
Pages 16354-16375
DOI: 10.3934/math.2024792

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Cite this article:
Wang P, Wang J. Hardy type identities and inequalities with divergence type operators on smooth metric measure spaces. AIMS Mathematics, 2024, 9(6): 16354-16375. https://doi.org/10.3934/math.2024792

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Received: 27 February 2024
Revised: 08 April 2024
Accepted: 29 April 2024
Published: 09 May 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)