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

• Autorzy: Eero Saksman , Tomás Soto
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Trace theorems; Sobolev spaces; Besov spaces; Triebel-Lizorkin spaces; hyperbolic filling

Kategorie tematyczne

• 42B35: Function spaces arising in harmonic analysis
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2017
• Tom: 5
• Numer: 1
• Strony: 98-115

Daty

wydano

2017-12-20

otrzymano

2017-08-22

zaakceptowano

2017-11-02

online

2017-12-22

Twórcy

autor

Eero Saksman

• ,

autor

Tomás Soto

• ,

Identyfikatory

DOI

10.1515/agms-2017-0006