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arXiv · 2209.04225

Generalised Hardy type and Rellich type inequalities on the Heisenberg group

Abimbola Abolarinwa·Michael Ruzhansky
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Abstract

This paper is primarily devoted to a class of interpolation inequalities of Hardy and Rellich types on the Heisenberg group $\mathbb{H}^n$. Consequently, several weighted Hardy type, Heisenberg-Pauli-Weyl uncertainty principle and Hardy-Rellich type inqualities are established on $\mathbb{H}^n$. Moreover, new weighted Sobolev type embeddings are derived. Finally, an integral inequality for vector fields in a domain of the Heisenberg group is obtained, leading to several specific weighted Hardy type inequalities by making careful choices of vector fields.

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Abimbola Abolarinwa, Michael Ruzhansky. 2022-09-09. Generalised Hardy type and Rellich type inequalities on the Heisenberg group. https://arxiv.org/abs/2209.04225

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