Lebesgue Points of Besov and Triebel–Lizorkin Spaces with Generalized Smoothness

In this article, the authors study the Lebesgue point of functions from Hajłasz–Sobolev, Besov, and Triebel–Lizorkin spaces with generalized smoothness on doubling metric measure spaces and prove that the exceptional sets of their Lebesgue points have zero capacity via the capacities related to thes...

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Main Authors:	Ziwei Li, Dachun Yang, Wen Yuan
Format:	article
Language:	EN
Published:	MDPI AG 2021
Subjects:	Hajłasz–Sobolev space Hajłasz–Besov space Hajłasz–Triebel–Lizorkin space generalized smoothness Lebesgue point capacity Mathematics QA1-939
Online Access:	https://doaj.org/article/c2f09e2e19ef4920b1c8c2141be91e07
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spelling	oai:doaj.org-article:c2f09e2e19ef4920b1c8c2141be91e072021-11-11T18:16:42ZLebesgue Points of Besov and Triebel–Lizorkin Spaces with Generalized Smoothness10.3390/math92127242227-7390https://doaj.org/article/c2f09e2e19ef4920b1c8c2141be91e072021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2724https://doaj.org/toc/2227-7390In this article, the authors study the Lebesgue point of functions from Hajłasz–Sobolev, Besov, and Triebel–Lizorkin spaces with generalized smoothness on doubling metric measure spaces and prove that the exceptional sets of their Lebesgue points have zero capacity via the capacities related to these spaces. In case these functions are not locally integrable, the authors also consider their generalized Lebesgue points defined via the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-medians instead of the classical ball integral averages and establish the corresponding zero-capacity property of the exceptional sets.Ziwei LiDachun YangWen YuanMDPI AGarticleHajłasz–Sobolev spaceHajłasz–Besov spaceHajłasz–Triebel–Lizorkin spacegeneralized smoothnessLebesgue pointcapacityMathematicsQA1-939ENMathematics, Vol 9, Iss 2724, p 2724 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Hajłasz–Sobolev space Hajłasz–Besov space Hajłasz–Triebel–Lizorkin space generalized smoothness Lebesgue point capacity Mathematics QA1-939
spellingShingle	Hajłasz–Sobolev space Hajłasz–Besov space Hajłasz–Triebel–Lizorkin space generalized smoothness Lebesgue point capacity Mathematics QA1-939 Ziwei Li Dachun Yang Wen Yuan Lebesgue Points of Besov and Triebel–Lizorkin Spaces with Generalized Smoothness
description	In this article, the authors study the Lebesgue point of functions from Hajłasz–Sobolev, Besov, and Triebel–Lizorkin spaces with generalized smoothness on doubling metric measure spaces and prove that the exceptional sets of their Lebesgue points have zero capacity via the capacities related to these spaces. In case these functions are not locally integrable, the authors also consider their generalized Lebesgue points defined via the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-medians instead of the classical ball integral averages and establish the corresponding zero-capacity property of the exceptional sets.
format	article
author	Ziwei Li Dachun Yang Wen Yuan
author_facet	Ziwei Li Dachun Yang Wen Yuan
author_sort	Ziwei Li
title	Lebesgue Points of Besov and Triebel–Lizorkin Spaces with Generalized Smoothness
title_short	Lebesgue Points of Besov and Triebel–Lizorkin Spaces with Generalized Smoothness
title_full	Lebesgue Points of Besov and Triebel–Lizorkin Spaces with Generalized Smoothness
title_fullStr	Lebesgue Points of Besov and Triebel–Lizorkin Spaces with Generalized Smoothness
title_full_unstemmed	Lebesgue Points of Besov and Triebel–Lizorkin Spaces with Generalized Smoothness
title_sort	lebesgue points of besov and triebel–lizorkin spaces with generalized smoothness
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/c2f09e2e19ef4920b1c8c2141be91e07
work_keys_str_mv	AT ziweili lebesguepointsofbesovandtriebellizorkinspaceswithgeneralizedsmoothness AT dachunyang lebesguepointsofbesovandtriebellizorkinspaceswithgeneralizedsmoothness AT wenyuan lebesguepointsofbesovandtriebellizorkinspaceswithgeneralizedsmoothness
_version_	1718431909367775232

Lebesgue Points of Besov and Triebel–Lizorkin Spaces with Generalized Smoothness

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