Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces
Analysis and Geometry in Metric Spaces, Tome 5 (2017) no. 1, pp. 98-115
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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.
Mots-clés :
Trace theorems, Sobolev spaces, Besov spaces, Triebel-Lizorkin spaces, hyperbolic filling
Saksman, Eero; Soto, Tomás. Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces. Analysis and Geometry in Metric Spaces, Tome 5 (2017) no. 1, pp. 98-115. http://geodesic.mathdoc.fr/item/AGMS_2017_5_1_a5/
@article{AGMS_2017_5_1_a5,
author = {Saksman, Eero and Soto, Tom\'as},
title = {Traces of {Besov,} {Triebel-Lizorkin} and {Sobolev} {Spaces} on {Metric} {Spaces}},
journal = {Analysis and Geometry in Metric Spaces},
pages = {98--115},
year = {2017},
volume = {5},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/AGMS_2017_5_1_a5/}
}