Generalised Hardy type and Rellich type inequalities on the Heisenberg group

IF 0.9 3区 数学 Q2 MATHEMATICS Journal of Pseudo-Differential Operators and Applications Pub Date : 2023-12-08 DOI:10.1007/s11868-023-00575-x
Abimbola Abolarinwa, Michael Ruzhansky
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引用次数: 2

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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海森堡群上的广义哈代型和雷利希型不等式
本文主要研究海森堡群 \(\mathbb {H}^n\)上的一类哈代型和雷利希型插值不等式。因此,在 \(\mathbb {H}^n\) 上建立了几个加权哈代型、海森堡-保利-韦尔不确定性原理和哈代-雷利希型不等式。此外,还导出了新的加权索波列夫型嵌入。最后,通过仔细选择向量场,得到了海森堡群域中向量场的积分不等式,从而得出了几个具体的加权哈代型不等式。
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来源期刊
CiteScore
2.20
自引率
9.10%
发文量
59
期刊介绍: The Journal of Pseudo-Differential Operators and Applications is a forum for high quality papers in the mathematics, applications and numerical analysis of pseudo-differential operators. Pseudo-differential operators are understood in a very broad sense embracing but not limited to harmonic analysis, functional analysis, operator theory and algebras, partial differential equations, geometry, mathematical physics and novel applications in engineering, geophysics and medical sciences.
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