Hastings studied Carleson measures for non-negative subharmonic functions on the polydisk and characterized them by a certain geometric condition relative to Lebesgue measure $\s$. Cima \& Wogen and Luecking proved analogous results for weighted Bergman spaces on the unit ball and other open subsets of $\mathC^n$. We consider a similar problem on a homogeneous tree, and study how the characterization and properties of Carleson measures for various function spaces depend on the choice of reference measure $\sigma$.

Cohen J., M., Colonna, F., Picardello, A.m., Singman, D. (2016). Bergman Spaces and Carleson Measures on Homogeneous Isotropic Trees. POTENTIAL ANALYSIS, 44(4), 745-766 [10.1007/s11118-015-9529-7].

### Bergman Spaces and Carleson Measures on Homogeneous Isotropic Trees

#### Abstract

Hastings studied Carleson measures for non-negative subharmonic functions on the polydisk and characterized them by a certain geometric condition relative to Lebesgue measure $\s$. Cima \& Wogen and Luecking proved analogous results for weighted Bergman spaces on the unit ball and other open subsets of $\mathC^n$. We consider a similar problem on a homogeneous tree, and study how the characterization and properties of Carleson measures for various function spaces depend on the choice of reference measure $\sigma$.
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Rilevanza internazionale
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Esperti anonimi
Settore MAT/05 - Analisi Matematica
English
Con Impact Factor ISI
Carleson measure, Bergman space, isotropic homogeneous trees, very regular transition operators, Green kernel, Poisson kernel
Cohen J., M., Colonna, F., Picardello, A.m., Singman, D. (2016). Bergman Spaces and Carleson Measures on Homogeneous Isotropic Trees. POTENTIAL ANALYSIS, 44(4), 745-766 [10.1007/s11118-015-9529-7].
Cohen J., M; Colonna, F; Picardello, Am; Singman, D
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/189245