Dyadic norm Besov-type spaces as trace spaces on regular trees

TL;DR

This paper investigates Besov-type function spaces on regular tree boundaries, demonstrating they serve as trace spaces for weighted Sobolev spaces through dyadic energy constructions.

Contribution

It introduces a new class of Besov-type spaces defined via dyadic energies on regular trees and establishes their role as trace spaces of weighted Sobolev spaces.

Findings

Besov-type spaces characterized by dyadic energies

Identification of these spaces as trace spaces of weighted Sobolev spaces

Correct dyadic energy choices are crucial for this characterization

Abstract

In this paper, we study function spaces defined via dyadic energies on the boundaries of regular trees. We show that correct choices of dyadic energies result in Besov-type spaces that are trace spaces of (weighted) first order Sobolev spaces.