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 Calderón–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.
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Acknowledgments
Work partially supported by the MIUR project “Dipartimenti di Eccellenza 2018-2022” (CUP E11G18000350001) and the Progetto GNAMPA 2020 “Fractional Laplacians and subLaplacians on Lie groups and trees”.
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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Levi, M., Santagati, F., Tabacco, A. et al. Analysis on Trees with Nondoubling Flow Measures. Potential Anal 58, 731–759 (2023). https://doi.org/10.1007/s11118-021-09957-6
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DOI: https://doi.org/10.1007/s11118-021-09957-6