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

Eero 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 -