Abstract
We consider an infinite homogeneous tree \(\mathcal V\) endowed with the usual metric d defined on graphs and a weighted measure μ. The metric measure space \((\mathcal V,d,\mu )\) 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(μ) on \((\mathcal V,d,\mu )\) and investigate some of its properties, focusing in particular on real interpolation properties and on boundedness of singular integrals on H 1(μ).
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Acknowledgements
Work partially supported by the MIUR project “Dipartimenti di Eccellenza 2018–2022” (CUP E11G18000350001). The authors are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).
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Arditti, L., Tabacco, A., Vallarino, M. (2020). Hardy Spaces on Weighted Homogeneous Trees. In: Boggiatto, P., et al. Advances in Microlocal and Time-Frequency Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-36138-9_2
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DOI: https://doi.org/10.1007/978-3-030-36138-9_2
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