Geodesic
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.

Voir la notice de l'article provenant de la source The Polish Digital Mathematics Library

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 
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     author = {Saksman, Eero and Soto, Tom\'as},
     title = {Traces of {Besov,} {Triebel-Lizorkin} and {Sobolev} {Spaces} on {Metric} {Spaces}},
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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/