Harmonic Bergman spaces on locally finite trees
Abstract
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.
Fields of Study & Subjects
Holomorphic and Operator Theory
Advanced Harmonic Analysis Research
Mathematical Analysis and Transform Methods
Publication details
- Journal / source
- Annali di Matematica Pura ed Applicata (1923 -)
- Volume
- 205
- Issue
- 4
- Pages
- 1705–1729
- Publication date
- 16 January 2026
- Language
- EN