Characterization of trace spaces on regular trees via dyadic norms. (English) Zbl 1469.46034
Summary: 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.
MSC:
| 46E36 | Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces |
| 05C05 | Trees |
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