Characterization of traces of smooth functions on Ahlfors regular sets

TL;DR

This paper generalizes the characterization of traces of Besov and Triebel-Lizorkin spaces from Ahlfors regular sets to d-regular sets with dimension between n-1 and n, using local polynomial approximations.

Contribution

It extends previous results on trace characterizations to a broader class of d-regular sets with new approximation methods.

Findings

Trace spaces characterized in terms of local polynomial approximations

Extension of results from Ahlfors n-regular sets to d-regular sets

Provides a framework for analyzing traces on more general fractal 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.