We consider an infinite homogeneous tree V endowed with the usual metric d defined on graphs and a weighted measure μ. The metric measure space (V, d, μ) 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 H1(μ) on (V, d, μ) and investigate some of its properties, focusing in particular on real interpolation properties and on boundedness of singular integrals on H1(μ).

Hardy Spaces on Weighted Homogeneous Trees / Arditti, L.; Tabacco, A.; Vallarino, M. (APPLIED AND NUMERICAL HARMONIC ANALYSIS). - In: Applied and Numerical Harmonic AnalysisSTAMPA. - [s.l] : Birkhauser, 2020. - ISBN 978-3-030-36137-2. - pp. 21-39 [10.1007/978-3-030-36138-9_2]

Hardy Spaces on Weighted Homogeneous Trees

Arditti L.;Tabacco A.;Vallarino M.
2020

Abstract

We consider an infinite homogeneous tree V endowed with the usual metric d defined on graphs and a weighted measure μ. The metric measure space (V, d, μ) 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 H1(μ) on (V, d, μ) and investigate some of its properties, focusing in particular on real interpolation properties and on boundedness of singular integrals on H1(μ).
978-3-030-36137-2
978-3-030-36138-9
Applied and Numerical Harmonic Analysis
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2831537