Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces

We establish trace theorems for function spaces defined on general Ahlfors regular metric spaces Z. The results cover the Triebel-Lizorkin spaces and the Besov spaces for smoothness indices s < 1, as well as the first order Hajłasz-Sobolev space M1,p(Z). They generalize the classical results from...

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Autores principales:	Saksman Eero, Soto Tomás
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2017
Materias:	trace theorems sobolev spaces besov spaces triebel-lizorkin spaces hyperbolic filling primary: 46e35 42b35 Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/7bbe4aace215422695e93a81069214c4
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spelling	oai:doaj.org-article:7bbe4aace215422695e93a81069214c42021-12-05T14:10:38ZTraces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces2299-327410.1515/agms-2017-0006https://doaj.org/article/7bbe4aace215422695e93a81069214c42017-12-01T00:00:00Zhttps://doi.org/10.1515/agms-2017-0006https://doaj.org/toc/2299-3274We establish trace theorems for function spaces defined on general Ahlfors regular metric spaces Z. The results cover the Triebel-Lizorkin spaces and the Besov spaces for smoothness indices s < 1, as well as the first order Hajłasz-Sobolev space M1,p(Z). They generalize the classical results from the Euclidean setting, since the traces of these function spaces onto any closed Ahlfors regular subset F ⊂ Z are Besov spaces defined intrinsically on F. Our method employs the definitions of the function spaces via hyperbolic fillings of the underlying metric space.Saksman EeroSoto TomásDe Gruyterarticletrace theoremssobolev spacesbesov spacestriebel-lizorkin spaceshyperbolic fillingprimary: 46e3542b35AnalysisQA299.6-433ENAnalysis and Geometry in Metric Spaces, Vol 5, Iss 1, Pp 98-115 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	trace theorems sobolev spaces besov spaces triebel-lizorkin spaces hyperbolic filling primary: 46e35 42b35 Analysis QA299.6-433
spellingShingle	trace theorems sobolev spaces besov spaces triebel-lizorkin spaces hyperbolic filling primary: 46e35 42b35 Analysis QA299.6-433 Saksman Eero Soto Tomás Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces
description	We establish trace theorems for function spaces defined on general Ahlfors regular metric spaces Z. The results cover the Triebel-Lizorkin spaces and the Besov spaces for smoothness indices s < 1, as well as the first order Hajłasz-Sobolev space M1,p(Z). They generalize the classical results from the Euclidean setting, since the traces of these function spaces onto any closed Ahlfors regular subset F ⊂ Z are Besov spaces defined intrinsically on F. Our method employs the definitions of the function spaces via hyperbolic fillings of the underlying metric space.
format	article
author	Saksman Eero Soto Tomás
author_facet	Saksman Eero Soto Tomás
author_sort	Saksman Eero
title	Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces
title_short	Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces
title_full	Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces
title_fullStr	Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces
title_full_unstemmed	Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces
title_sort	traces of besov, triebel-lizorkin and sobolev spaces on metric spaces
publisher	De Gruyter
publishDate	2017
url	https://doaj.org/article/7bbe4aace215422695e93a81069214c4
work_keys_str_mv	AT saksmaneero tracesofbesovtriebellizorkinandsobolevspacesonmetricspaces AT sototomas tracesofbesovtriebellizorkinandsobolevspacesonmetricspaces
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Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces

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