On traces of general decomposition spaces

Abstract

The decomposition space approach is a general method to construct smoothness spaces on \(\mathbb{R }^d\) that include Besov, Triebel–Lizorkin, modulation, and \(\alpha \)-modulation spaces as special cases. This method also handles isotropic and an-isotropic spaces within the same framework. In this paper we consider a trace theorem for general decomposition type smoothness spaces. The result is based on a simple geometric estimate related to the structure of coverings of the frequency space used in the construction of decomposition spaces.