Hardy spaces on weighted homogeneous trees
Functional Analysis
2019-02-26 v1
Abstract
We consider an infinite homogeneous tree V endowed with the usual metric d defined on graphs and a weighted measure \mu. The metric measure space V,d,\mu) is nondoubling and of exponential growth, hence the classical theory of Hardy spaces does not apply in this setting. We construct an atomic Hardy space H^1 on (V,d,\mu) and investigate some of its properties, focusing in particular on real interpolation properties and on boundedness of singular integrals on H^1.
Keywords
Cite
@article{arxiv.1902.09273,
title = {Hardy spaces on weighted homogeneous trees},
author = {Laura Arditti and Anita Tabacco and Maria Vallarino},
journal= {arXiv preprint arXiv:1902.09273},
year = {2019}
}
Comments
17 pages; 2 figures