Affiliation:
1. Department of Mathematics and Statistics, University of Helsinki, PO Box 68, FI-00014 Helsinki , Finland
Abstract
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.
Subject
Applied Mathematics,Geometry and Topology,Analysis
Reference37 articles.
1. [1] M. Bonk and E. Saksman: Sobolev spaces and hyperbolic fillings, J. Reine Angew. Math., to appear.
2. [2] M. Bonk, E. Saksman and T. Soto: Triebel-Lizorkin spaces on metric spaces via hyperbolic fillings, Indiana Univ. Math. J., to appear.
3. [3] M. Bourdon and H. Pajot: Cohomologie lp et espaces de Besov, J. Reine Angew. Math. 558 (2003), 85-108.
4. [4] A. Caetano and D. Haroske: Traces of Besov spaces on fractal h-sets and dichotomy results, Studia Math. 231 (2015), no. 2, 117-147.
5. [5] M. Frazier and B. Jawerth: Decomposition of Besov spaces, Indiana Univ. Math. J. 34 (1985), no. 4, 777-799.
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