Hardy inequalities on metric measure spaces, IV: The case p=1

IF 1 3区数学 Q1 MATHEMATICS

Forum Mathematicum Pub Date : 2024-01-14 DOI:10.1515/forum-2023-0319

Michael Ruzhansky, Anjali Shriwastawa, Bankteshwar Tiwari

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引用次数: 0

Abstract

In this paper, we investigate the two-weight Hardy inequalities on metric measure space possessing polar decompositions for the case p = 1

{p=1}

and 1 ≤ q < ∞

{1\leq q<\infty}

. This result complements the Hardy inequalities obtained in [M. Ruzhansky and D. Verma, Hardy inequalities on metric measure spaces, Proc. Roy. Soc. A. 475 2019, 2223, Article ID 20180310] in the case 1 < p ≤ q < ∞

{1<p\leq q<\infty}

. The case p = 1

{p=1}

requires a different argument and does not follow as the limit of known inequalities for p > 1

{p>1}

. As a byproduct, we also obtain the best constant in the established inequality. We give examples obtaining new weighted Hardy inequalities on homogeneous Lie groups, on hyperbolic spaces and on Cartan–Hadamard manifolds for the case p = 1

{p=1}

and 1 ≤ q < ∞

{1\leq q<\infty}

查看原文本刊更多论文

度量空间上的哈代不等式，IV：p=1 的情况

在本文中，我们研究了具有极性分解的度量空间上的两重哈代不等式，即 p = 1 {p=1} 和 1 ≤ q < ∞ {1\leq q<\infty} 的情况。这一结果是对 [M. Ruzhansky 和 D. Ruzhansky] 中得到的哈代不等式的补充。Ruzhansky and D. Verma, Hardy inequalities on metric measure spaces, Proc.Roy.Soc. A. 475 2019, 2223, Article ID 20180310] 中 1 < p ≤ q < ∞ {1<p\leq q<\infty} 的情况。p = 1 {p=1}的情况需要不同的论证，并不是 p > 1 {p>1}的已知不等式的极限。作为副产品，我们还得到了既定不等式中的最佳常数。我们举例说明了在 p = 1 {p=1} 和 1 ≤ q < ∞ {1\leq q<\infty} 的情况下，同质李群、双曲空间和 Cartan-Hadamard 流形上新的加权哈代不等式。

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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来源期刊

Forum Mathematicum 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Forum Mathematicum is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.