Characterization of trace spaces on regular trees via dyadic norms

Abstract

In this paper, we study the traces of Orlicz-Sobolev spaces on a regular rooted tree. After giving a dyadic decomposition of the boundary of the regular tree, we present a characterization on the trace spaces of those first order Orlicz-Sobolev spaces whose Young function is of the form $t^p\log^\lambda(e+t)$, based on integral averages on dyadic elements of the dyadic decomposition.