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

Analysis and Geometry in Metric Spaces (2017)

- Volume: 5, Issue: 1, page 98-115
- ISSN: 2299-3274

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topEero Saksman, and Tomás Soto. "Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces." Analysis and Geometry in Metric Spaces 5.1 (2017): 98-115. <http://eudml.org/doc/288572>.

@article{EeroSaksman2017,

abstract = {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.},

author = {Eero Saksman, Tomás Soto},

journal = {Analysis and Geometry in Metric Spaces},

keywords = {Trace theorems; Sobolev spaces; Besov spaces; Triebel-Lizorkin spaces; hyperbolic filling},

language = {eng},

number = {1},

pages = {98-115},

title = {Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces},

url = {http://eudml.org/doc/288572},

volume = {5},

year = {2017},

}

TY - JOUR

AU - Eero Saksman

AU - Tomás Soto

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

JO - Analysis and Geometry in Metric Spaces

PY - 2017

VL - 5

IS - 1

SP - 98

EP - 115

AB - 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.

LA - eng

KW - Trace theorems; Sobolev spaces; Besov spaces; Triebel-Lizorkin spaces; hyperbolic filling

UR - http://eudml.org/doc/288572

ER -

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