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arXiv · 2504.07581

H\"older continuity and composition operators in pluriharmonic Bloch spaces

Jie Huang·Suman Das·Antti Rasila
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Abstract

We show a H\"older estimate of order $1/n$ for pluriharmonic Bloch mappings in the unit ball $\mathbb{B}^n \subset \mathbb{C}^n$ with respect to the Bergman metric. We apply this to obtain a sufficient condition for the composition operator on the pluriharmonic Bloch space to be bounded below. As a partial converse, we also give a necessary condition for the boundedness below of the composition operator on the Bloch space of holomorphic mappings in $\mathbb{B}^n$.

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Jie Huang, Suman Das, Antti Rasila. 2025-04-10. H\"older continuity and composition operators in pluriharmonic Bloch spaces. https://doi.org/10.1007/s13324-026-01258-8

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