Some hardy type inequalities with finsler norms

Duy, Nguyen Tuan

doi:10.1515/ms-2017-0470

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2022

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“…More interestingly, a pair of weight functions was introduced in [24], where the weights have to satisfy certain compatibility conditions for the inequalities to hold true. In a related development, frank efforts from different authors (e.g., [25][26][27]) yielded various Hardy-type inequalities on Finslerian manifolds.…”

Section: Introductionmentioning

confidence: 99%

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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