Characterization of traces of smooth functions on Ahlfors regular sets

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.

37 pages

References in corpus (1)

• Smoothness spaces of higher order on lower dimensional subsets of the Euclidean space

Cited by in corpus (4)

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• Hardy inequalities in Triebel-Lizorkin spaces II. Aikawa dimension
• Hardy inequalities in Triebel-Lizorkin spaces