Lipschitz continuity and composition operators in pluriharmonic Bloch spaces

2025/04/10 by Huang, Jie, Das, Suman, Rasila, Antti
#Complex Variables (math.CV) #FOS: Mathematics #Primary: 32A18 #Secondary: 31C10

paper · doi:10.48550/arxiv.2504.07581

Abstract

We study the Lipschitz continuity of pluriharmonic Bloch mappings in the unit ball \mathbbBⁿ with respect to the Bergman metric. We apply this to obtain a sufficient condition such that the composition operator on the pluriharmonic Bloch space is bounded below. As a partial converse, we also give a necessary condition for the boundedness (from below) of the composition operator on the Bloch space of holomorphic mappings in \mathbbBⁿ.

Related

• Characterizations of composition operators on Bloch and Hardy type spaces
• Equivalent moduli of continuity, Bloch's theorem for pluriharmonic mappings in \mathbbBⁿ
• The Landau-Bloch type theorems for certain class of holomorphic and pluriharmonic mappings in \mathbbcⁿ
• Composition operators on Bloch and Hardy type spaces
• Composition operators on the spaces of Harmonic Bloch functions