Horocyclic harmonic Bergman spaces on homogeneous trees

2023/09/26 by Filippo De Mari, Matteo Monti, De Mari, Filippo +3 · 1 citation
Mathematics · #05C05 #43A85 #46E22 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2309.15047

openalex publication_date 2023/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main focus of this contribution is on the harmonic Bergman spaces B_α^p on the q-homogeneous tree \mathfrakX_q endowed with a family of measures σ_α that are constant on the horocycles tangent to a fixed boundary point and turn out to be doubling with respect to the corresponding horocyclic Gromov distance. A central role is played by the reproducing kernel Hilbert space B_α² for which we find a natural orthonormal basis and formulae for the kernel. We also consider the atomic Hardy space and the bounded mean oscillation space. Appealing to an adaptation of Calderón-Zygmund theory and to standard boundedness results for integral operators on L^p_α spaces with Hörmander-type kernels, we determine the boundedness properties of the Bergman projection.

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• Harmonic Bergman spaces on locally finite trees

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