Harmonic Bergman spaces on locally finite trees

2025/05/06 by Alessandro Ottazzi, Ottazzi, Alessandro, Federico Santagati +1
Arts and Humanities · Mathematics · #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Literature and Cultural Memory

paper · pdf · doi:10.48550/arxiv.2505.03479

openalex publication_date 2025/05/06 · openalex created_date 2025/10/16 · openalex updated_date 2026/08/01

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.

Citations

• Endpoint estimates and sparse domination in nonhomogeneous trees
• Carleson measures on locally finite trees
• Triangular maximal operators on locally finite trees
• Riesz transform and spectral multipliers for the flow Laplacian on nonhomogeneous trees
• Horocyclic harmonic Bergman spaces on homogeneous trees
• Hardy-Littlewood maximal operators on trees with bounded geometry
• Harmonic Bergman Spaces on the Real Hyperbolic Ball: Atomic Decomposition, Interpolation and Inclusion Relations
• Harmonic Bergman projectors on homogeneous trees
• Nondoubling Calderón-Zygmund theory -a dyadic approach-
• A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderon-Zygmund decomposition

Related

• Harmonic Bergman projectors on homogeneous trees
• Horocyclic harmonic Bergman spaces on homogeneous trees
• Korevaar-Schoen and heat kernel characterizations of Sobolev and BV spaces on local trees
• Riesz transform and spectral multipliers for the flow Laplacian on nonhomogeneous trees
• A_p weights on nonhomogeneous trees equipped with measures of exponential growth