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

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.

Keywords

• trace theorems
• sobolev spaces
• besov spaces
• triebel-lizorkin spaces
• hyperbolic filling
• primary: 46e35
• 42b35