Characterization of traces of smooth functions on Ahlfors regular sets

Lizaveta Ihnatsyeva; Antti V. Vähäkangas

doi:10.1016/j.jfa.2013.07.006

Characterization of traces of smooth functions on Ahlfors regular sets

Lizaveta Ihnatsyeva, Antti V. Vähäkangas^*

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

Research output: Contribution to journal › Article › Scientific › peer-review

10 Citations (Scopus)

Abstract

We extend the results of P. Shvartsman on characterizing the traces of Besov and Triebel-Lizorkin spaces on Ahlfors n-regular sets to the case of d-regular sets, n-. 1. <. d<. n. The characterizations of trace spaces are given in terms of local polynomial approximations.

Original language	English
Pages (from-to)	1870-1915
Number of pages	46
Journal	Journal of Functional Analysis
Volume	265
Issue number	9
DOIs	https://doi.org/10.1016/j.jfa.2013.07.006
Publication status	Published - 1 Nov 2013
MoE publication type	A1 Journal article-refereed

Keywords

Ahlfors d-regular set
Besov space
Local polynomial approximation
Trace theorem
Triebel-Lizorkin space

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10.1016/j.jfa.2013.07.006

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abstract = "We extend the results of P. Shvartsman on characterizing the traces of Besov and Triebel-Lizorkin spaces on Ahlfors n-regular sets to the case of d-regular sets, n-. 1. <. d<. n. The characterizations of trace spaces are given in terms of local polynomial approximations.",

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N2 - We extend the results of P. Shvartsman on characterizing the traces of Besov and Triebel-Lizorkin spaces on Ahlfors n-regular sets to the case of d-regular sets, n-. 1. <. d<. n. The characterizations of trace spaces are given in terms of local polynomial approximations.

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KW - Besov space

KW - Local polynomial approximation

KW - Trace theorem

KW - Triebel-Lizorkin space

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