Some Inequalities of Hardy Type Related to Witten–Laplace Operator on Smooth Metric Measure Spaces

Yanlin Li, Abimbola Abolarinwa, Ali H. Alkhaldi and Akram Ali ()
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Yanlin Li: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Abimbola Abolarinwa: Department of Mathematics, University of Lagos, Akoka, Lagos 101017, Nigeria
Ali H. Alkhaldi: Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
Akram Ali: Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia

Mathematics, 2022, vol. 10, issue 23, 1-13

Abstract: A complete Riemannian manifold equipped with some potential function and an invariant conformal measure is referred to as a complete smooth metric measure space. This paper generalizes some integral inequalities of the Hardy type to the setting of a complete non-compact smooth metric measure space without any geometric constraint on the potential function. The adopted approach highlights some criteria for a smooth metric measure space to admit Hardy inequalities related to Witten and Witten p -Laplace operators. The results in this paper complement in several aspect to those obtained recently in the non-compact setting.

Keywords: Riemannian manifold; Hardy inequality; uncertainty principle; elliptic operators; Rellich inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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