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

TL;DR

This paper investigates higher-order smoothness spaces on lower-dimensional subsets of Euclidean space, focusing on Sobolev-type spaces defined via maximal functions and their relation to classical Sobolev space traces.

Contribution

It introduces and analyzes Sobolev-type spaces on Ahlfors regular sets, establishing their connection with classical Sobolev space traces.

Findings

Characterization of Sobolev spaces on Ahlfors regular sets

Relations between maximal function-based spaces and classical Sobolev traces

New insights into higher-order smoothness on fractal-like sets

Abstract

We study Sobolev type spaces defined in terms of sharp maximal functions on Ahlfors regular subsets of the Euclidean space and the relation between these spaces and traces of classical Sobolev spaces.