一些$\boldsymbol {L^p}$ -HARDY和$\boldsymbol {L^p}$ -RELLICH型带余项不等式

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of the Australian Mathematical Society Pub Date : 2021-06-22 DOI:10.1017/S1446788721000100

Yongyang Jin, Shoufeng Shen

引用次数: 0

摘要

摘要本文在黎曼流形的有界域上得到了改进的$L^p$ -Hardy不等式和$L^p$ -Rellich不等式。对于Cartan-Hadamard流形，我们证明了具有尖锐常数和权值为黎曼距离双曲函数的不等式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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SOME $\boldsymbol {L^p}$ -HARDY AND $\boldsymbol {L^p}$ -RELLICH TYPE INEQUALITIES WITH REMAINDER TERMS

Abstract In this paper we obtain some improved $L^p$ -Hardy and $L^p$ -Rellich inequalities on bounded domains of Riemannian manifolds. For Cartan–Hadamard manifolds we prove the inequalities with sharp constants and with weights being hyperbolic functions of the Riemannian distance.

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来源期刊

Journal of the Australian Mathematical Society 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The Journal of the Australian Mathematical Society is the oldest journal of the Society, and is well established in its coverage of all areas of pure mathematics and mathematical statistics. It seeks to publish original high-quality articles of moderate length that will attract wide interest. Papers are carefully reviewed, and those with good introductions explaining the meaning and value of the results are preferred. Published Bi-monthly Published for the Australian Mathematical Society