March 27, 2024Open Access

Harmonic Bloch space on the real hyperbolic ball

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Abstract

Abstract We study the Bloch and the little Bloch spaces of harmonic functions on the real hyperbolic ball. We show that the Bergman projections from L^ ({B}) L ∞ (B) to {B} B, and from C₀ ({B}) C 0 (B) to {B}₀ B 0 are onto. We verify that the dual space of the hyperbolic harmonic Bergman space {B}¹_ B α 1 is {B} B and its predual is {B}₀ B 0. Finally, we obtain atomic decompositions of Bloch functions as series of Bergman reproducing kernels.

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A. Ersin Üreyen (Wed,) studied this question.

synapsesocial.com/papers/68e72309b6db64358769cec5 https://doi.org/https://doi.org/10.1007/s43034-024-00335-y

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