The refinement and generalization of Hardy’s inequality in Sobolev space

In this paper, we refine the proof of Hardy’s inequality in (Evans in Partial Differential Equations, 2010, Hardy in Inequalities, 1952) and extend Hardy’s inequality from two aspects. That is to say, we extend the integral estimation function from [Formula: see text] to [Formula: see text] with sui...

Descripción completa

Detalles Bibliográficos
Autores principales: Xue, Xiaomin, Li, Fushan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6267400/
https://www.ncbi.nlm.nih.gov/pubmed/30839848
http://dx.doi.org/10.1186/s13660-018-1922-5
_version_ 1783376066696445952
author Xue, Xiaomin
Li, Fushan
author_facet Xue, Xiaomin
Li, Fushan
author_sort Xue, Xiaomin
collection PubMed
description In this paper, we refine the proof of Hardy’s inequality in (Evans in Partial Differential Equations, 2010, Hardy in Inequalities, 1952) and extend Hardy’s inequality from two aspects. That is to say, we extend the integral estimation function from [Formula: see text] to [Formula: see text] with suitable [Formula: see text] and extend the space dimension from [Formula: see text] to [Formula: see text] . Hardy’s inequality in (Evans in Partial Differential Equations, 2010, Hardy in Inequalities, 1952) is the special case of our results.
format Online
Article
Text
id pubmed-6267400
institution National Center for Biotechnology Information
language English
publishDate 2018
publisher Springer International Publishing
record_format MEDLINE/PubMed
spelling pubmed-62674002018-12-11 The refinement and generalization of Hardy’s inequality in Sobolev space Xue, Xiaomin Li, Fushan J Inequal Appl Research In this paper, we refine the proof of Hardy’s inequality in (Evans in Partial Differential Equations, 2010, Hardy in Inequalities, 1952) and extend Hardy’s inequality from two aspects. That is to say, we extend the integral estimation function from [Formula: see text] to [Formula: see text] with suitable [Formula: see text] and extend the space dimension from [Formula: see text] to [Formula: see text] . Hardy’s inequality in (Evans in Partial Differential Equations, 2010, Hardy in Inequalities, 1952) is the special case of our results. Springer International Publishing 2018-11-28 2018 /pmc/articles/PMC6267400/ /pubmed/30839848 http://dx.doi.org/10.1186/s13660-018-1922-5 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Xue, Xiaomin
Li, Fushan
The refinement and generalization of Hardy’s inequality in Sobolev space
title The refinement and generalization of Hardy’s inequality in Sobolev space
title_full The refinement and generalization of Hardy’s inequality in Sobolev space
title_fullStr The refinement and generalization of Hardy’s inequality in Sobolev space
title_full_unstemmed The refinement and generalization of Hardy’s inequality in Sobolev space
title_short The refinement and generalization of Hardy’s inequality in Sobolev space
title_sort refinement and generalization of hardy’s inequality in sobolev space
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6267400/
https://www.ncbi.nlm.nih.gov/pubmed/30839848
http://dx.doi.org/10.1186/s13660-018-1922-5
work_keys_str_mv AT xuexiaomin therefinementandgeneralizationofhardysinequalityinsobolevspace
AT lifushan therefinementandgeneralizationofhardysinequalityinsobolevspace
AT xuexiaomin refinementandgeneralizationofhardysinequalityinsobolevspace
AT lifushan refinementandgeneralizationofhardysinequalityinsobolevspace

Ejemplares similares