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arXiv · 2410.23047

Endpoint estimates and sparse domination in nonhomogeneous trees

José M. Conde-Alonso·Filippo De Mari·Matteo Monti·Elena Rizzo·Maria Vallarino
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Abstract

We prove endpoint and sparse-like bounds for Bergman projectors on nonhomogeneous, radial trees $X$ that model manifolds with possibly unbounded geometry. The natural Bergman measures on $X$ may fail to be doubling, and even locally doubling, with respect to the right metric in our setting. Weighted consequences of our sparse domination results are also considered, and are in line with the known results in the disk. Our endpoint results are partly a consequence of a new Calder\'on-Zygmund theory for discrete, non-locally doubling metric spaces.

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José M. Conde-Alonso, Filippo De Mari, Matteo Monti, Elena Rizzo, Maria Vallarino. 2024-10-30. Endpoint estimates and sparse domination in nonhomogeneous trees. https://arxiv.org/abs/2410.23047

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