关于 $${\mathbb {R}}^{n-m}} times {\mathbb {R}}^{n}$$ 的反向 Hardy-Littlewood-Sobolev 型不等式

IF 1.1 3区数学 Q1 MATHEMATICS

Results in Mathematics Pub Date : 2024-08-03 DOI:10.1007/s00025-024-02227-y

Xiang Li, Minbo Yang

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引用次数: 0

摘要

本文将建立不同维空间上的反向 Hardy-Littlewood-Sobolev 不等式，并证明最佳常数的极值函数的存在性。此外，我们还研究了极值函数的正则性，并为积分系统解的存在提供了必要条件。最后，我们对极值函数进行了分类。

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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Reversed Hardy-Littlewood-Sobolev Type Inequality on $${\mathbb {R}}^{n-m}\times {\mathbb {R}}^{n}$$

In this paper, we are going to establish a reversed Hardy–Littlewood–Sobolev inequality on different dimensional space and prove the existence of extremal functions for the best constant. Furthermore, we investigate the regularity of extremal functions and provide a necessary conditions for the existence of solutions of the integral systems. Finally, we classify the extremal functions.

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来源期刊

Results in Mathematics 数学-数学

CiteScore

1.90

自引率

4.50%

发文量

198

审稿时长

6-12 weeks

期刊介绍： Results in Mathematics (RM) publishes mainly research papers in all fields of pure and applied mathematics. In addition, it publishes summaries of any mathematical field and surveys of any mathematical subject provided they are designed to advance some recent mathematical development.