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June 2018 Fractal functions with no radial limits in Bergman spaces on trees
Joel M. COHEN, Flavia COLONNA, Massimo A. PICARDELLO, David SINGMAN
Hokkaido Math. J. 47(2): 269-289 (June 2018). DOI: 10.14492/hokmj/1529308819

Abstract

For each $p \gt 0$ we provide the construction of a harmonic function on a homogeneous isotropic tree $T$ in the Bergman space $A^p(\sigma)$ with no finite radial limits anywhere. Here, $\sigma$ is an analogue of the Lebesgue measure on the tree. With the appropriate modifications, the construction yields a function in $A^1(\sigma)$ when $T$ is a rooted radial tree such that the number of forward neighbors increases so slowly that their reciprocals are not summable.

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Joel M. COHEN. Flavia COLONNA. Massimo A. PICARDELLO. David SINGMAN. "Fractal functions with no radial limits in Bergman spaces on trees." Hokkaido Math. J. 47 (2) 269 - 289, June 2018. https://doi.org/10.14492/hokmj/1529308819

Information

Published: June 2018
First available in Project Euclid: 18 June 2018

zbMATH: 06901706
MathSciNet: MR3815293
Digital Object Identifier: 10.14492/hokmj/1529308819

Subjects:
Primary: 05C05
Secondary: 31A05 , 60J45

Keywords: Bergman space , Harmonic function , homogeneous tree , radial tree

Rights: Copyright © 2018 Hokkaido University, Department of Mathematics

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Vol.47 • No. 2 • June 2018
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