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

Pengyan Wang; Jiahao Wang; Pengyan Wang; Jiahao Wang

doi:10.3934/math.2024792

AIMS Mathematics

2024, Volume 9, Issue 6: 16354-16375. doi: 10.3934/math.2024792

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Research article

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

Received: 27 February 2024 Revised: 08 April 2024 Accepted: 29 April 2024 Published: 09 May 2024
MSC : 53C21, 26D10

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.
- Hardy type inequality,
- Hardy type identity,
- smooth metric measure space,
- divergence type operator
Citation: Pengyan Wang, Jiahao Wang. Hardy type identities and inequalities with divergence type operators on smooth metric measure spaces[J]. AIMS Mathematics, 2024, 9(6): 16354-16375. doi: 10.3934/math.2024792

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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.

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