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arXiv · 1606.08729

Traces of Besov, Triebel-Lizorkin and Sobolev spaces on metric spaces

Eero Saksman·Tomás Soto
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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 Haj{\l}asz-Sobolev space $M^{1,p}(Z)$. They generalize the classical results from the Euclidean setting, since the traces of these function spaces onto any closed Ahlfors regular subset $F \subset Z$ are Besov spaces defined intrinsically on $F$. Our method employs the definitions of the function spaces via hyperbolic fillings of the underlying metric space.

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Eero Saksman, Tomás Soto. 2016-06-28. Traces of Besov, Triebel-Lizorkin and Sobolev spaces on metric spaces. https://arxiv.org/abs/1606.08729

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