On fractional inequalities on metric measure spaces with polar decomposition-Reference-Cited by-同舟云学术

On fractional inequalities on metric measure spaces with polar decomposition

Published:2024-07-13 Issue: Volume: Page:
ISSN:0933-7741
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Kassymov Aidyn¹^ORCID,Ruzhansky Michael²^ORCID,Zaur Gulnur³^ORCID

Affiliation:

1. 374528 Institute of Mathematics and Mathematical Modeling , 28 Shevchenko str., 050010 Almaty , Kazakhstan

2. Department of Mathematics: Analysis, Logic and Discrete Mathematics , Ghent University , Ghent , Belgium , and School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom

3. 374528 Institute of Mathematics and Mathematical Modeling , 28 Shevchenko str., 050010; and Al-Farabi Kazakh National University, 71 Al-Farabi ave., 050040 Almaty , Kazakhstan

Abstract

Abstract 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.

Funder

Fonds Wetenschappelijk Onderzoek

Universiteit Gent

Engineering and Physical Sciences Research Council

Ministry of Education and Science of the Republic of Kazakhstan

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/forum-2024-0056/pdf

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