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arXiv · 2505.03479

Harmonic Bergman spaces on locally finite trees

Alessandro Ottazzi·Federico Santagati
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Abstract

We define the harmonic Bergman space on locally finite trees with respect to a suitable probabilistic Laplacian and a class of weighted flow measures. We characterise the corresponding Bergman projection and prove that it is bounded on $L^p$ for every $p>1$, and of weak type $(1,1)$. We also prove necessary and sufficient conditions for the $L^p$-boundedness of the extension of a class of Toeplitz-type operators.

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Alessandro Ottazzi, Federico Santagati. 2025-05-06. Harmonic Bergman spaces on locally finite trees. https://arxiv.org/abs/2505.03479

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