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arXiv · 2207.13140

$\mathcal H$-Harmonic Bergman Projection on the Hyperbolic Ball

A. Ersin Üreyen
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Abstract

We determine precisely when the Bergman projection $P_β$ is bound\-ed from Lebesgue spaces $L^p_α$ to weighted Bergman spaces $\mathcal B^p_α$ of $\mathcal H$-harmonic functions on the hyperbolic ball, and verify a recent conjecture of M. Stoll. We obtain upper estimates for the reproducing kernel of the $\mathcal H$-harmonic Bergman space $\mathcal B^2_α$ and its partial derivatives. We also consider the projection from $L^\infty$ to the Bloch space $\mathcal B$ of $\mathcal H$-harmonic functions.

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A. Ersin Üreyen. 2022-07-26. $\mathcal H$-Harmonic Bergman Projection on the Hyperbolic Ball. https://doi.org/10.1016/j.jmaa.2022.126802

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