Weighted Hardy and Rellich type inequalities on Riemannian manifolds

Kömbe, Ismail; Yener, Abdullah

doi:10.1002/mana.201500237

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2017

2024

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Cited by 6 publications

(1 citation statement)

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“…Later, Kombe-Özaydin [17] (see also Kombe-Özaydin [18] and Kombe-Yener [19]) extended Carron's result to the general case 1 < p < ∞. In these references, the authors proved several Hardy-type, Rellich-type and uncertainty principle inequalities on manifolds satisfying certain geometric restrictions.…”

Section: Introductionmentioning

confidence: 95%

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

Abolarinwa

Alkhaldi

et al. 2022

Mathematics

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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.

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Section: Introductionmentioning

confidence: 95%