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.

arXiv comment23 pages

References in corpus (6)

• Geometric analysis on Cantor sets and trees
• Trace and extension theorems for Sobolev-type functions in metric spaces
• Dyadic norm Besov-type spaces as trace spaces on regular trees
• Besov spaces via hyperbolic fillings
• Traces of Newton-Sobolev, Hajlasz-Sobolev and BV functions on metric spaces
• A Characterization of Hajłasz-Sobolev and Triebel-Lizorkin Spaces via Grand Littlewood-Paley Functions