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.
@article{bwmeta1.element.doi-10_1515_agms-2017-0006,
author = {Eero Saksman and Tom\'as Soto},
title = {Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces},
journal = {Analysis and Geometry in Metric Spaces},
volume = {5},
year = {2017},
pages = {98-115},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_agms-2017-0006}
}
Eero Saksman; Tomás Soto. Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces. Analysis and Geometry in Metric Spaces, Tome 5 (2017) pp. 98-115. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_agms-2017-0006/