关于有极性分解的度量空间上的分数不等式

IF 1 3区数学 Q1 MATHEMATICS

Forum Mathematicum Pub Date : 2024-07-12 DOI:10.1515/forum-2024-0056

Aidyn Kassymov, Michael Ruzhansky, Gulnur Zaur

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引用次数: 0

摘要

本文证明了可极化度量空间上的分数哈代不等式。1 < p ≤ q < ∞ 1<p\leq q<\infty 的积分哈代不等式在证明中起着关键作用。此外，我们还证明了公度量空间上的分数哈代-索博廖夫型不等式。此外，我们还提出了公度量空间上的对数 Hardy-Sobolev 型不等式和分数纳什型不等式。此外，我们还介绍了在均质群和海森堡群上的应用。

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On fractional inequalities on metric measure spaces with polar decomposition

In this paper, we prove the fractional Hardy inequality on polarisable metric measure spaces. The integral Hardy inequality for 1 < p ≤ q < ∞

1<p\leq q<\infty

is playing a key role in the proof. Moreover, we also prove the fractional Hardy–Sobolev type inequality on metric measure spaces. In addition, logarithmic Hardy–Sobolev and fractional Nash type inequalities on metric measure spaces are presented. In addition, we present applications on homogeneous groups and on the Heisenberg group.

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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.