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

Abstract

Abstract. We study Sobolev type spaces defined in terms of sharp maximal functions on Ahlfors regular subsets of R n and the relation between these spaces and traces of classical Sobolev spaces. This extends in a certain way the results of Shvartsman [20] to the case of lower dimensional subsets of the Euclidean space.