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).
2020
978-3-030-36137-2
978-3-030-36138-9
Applied and Numerical Harmonic Analysis
File in questo prodotto:
File Dimensione Formato  
ArdittiTabaccoVallarinoVF.pdf

Open Access dal 05/04/2021

Tipologia: 2. Post-print / Author's Accepted Manuscript
Licenza: PUBBLICO - Tutti i diritti riservati
Dimensione 504.68 kB
Formato Adobe PDF
504.68 kB Adobe PDF Visualizza/Apri
arditti-tabacco-vallarino.pdf

non disponibili

Tipologia: 2a Post-print versione editoriale / Version of Record
Licenza: Non Pubblico - Accesso privato/ristretto
Dimensione 389.49 kB
Formato Adobe PDF
389.49 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2831537