Analysis on trees with nondoubling flow measures

TL;DR

This paper develops a Calderon-Zygmund theory for trees with nondoubling flow measures, defining BMO and Hardy spaces, and extending classical harmonic analysis results to this non-standard setting.

Contribution

It introduces a novel harmonic analysis framework for trees with nondoubling measures, including BMO and Hardy spaces, and extends classical Calderon-Zygmund theory.

Findings

Established Calderon-Zygmund theory for nondoubling measures on trees

Defined BMO and Hardy spaces in this new setting

Proved key properties extending classical harmonic analysis results

Abstract

We consider trees with root at infinity endowed with flow measures, which are nondoubling measures of at least exponential growth and which do not satisfy the isoperimetric inequality. In this setting, we develop a Calderon-Zygmund theory and we define BMO and Hardy spaces, proving a number of desired results extending the corresponding theory as known in more classical settings.