Bergman Spaces and Carleson Measures on Homogeneous Isotropic Trees |
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Authors: | Joel M Cohen Flavia Colonna Massimo A Picardello David Singman |
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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 σ. Cima & Wogen and Luecking proved analogous results for weighted Bergman spaces on the unit ball and other open subsets of \(\mathbb {C}^{n}\). 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 σ. |
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