Hölder Continuity and Boundedness of Composition Operators on Pluriharmonic $α$-Bloch Spaces
Year: 2026
Type: preprint
Abstract: In this paper, we study the metric properties of pluriharmonic $α$-Bloch-type mappings $f=h+\overline{g}\in\mathcal{H}(\mathbb{B}^{n},\mathbb{C}^{n})$ on the unit ball $\mathbb{B}^{n}\subset\mathbb{C}^{n}$. By synthesizing local real-part estimates with the subharmonicity of $\log(\vert{} \det Dh(z) \vert{} + \vert{} \det Dg(z) \vert{})$ along hyperbolic geodesics, we establish a globalized non-trivial lower bound across the entire unit ball $\mathbb{B}^{n}$. Using this structural decay estimate, we prove that the invariant weight quantity $D_{f}^{n,α}(z)$ satisfies a global Hölder continuity estimate of order $1/n$ with respect to the Bergman metric $β$. Furthermore, we investigate composition operators $C_φ(f)=f\circφ$ induced by holomorphic self-mappings $φ\in\mathcal{A}(\mathbb{B}^{n},\mathbb{B}^{n})$. We establish both sharp sufficient and necessary sampling conditions for $C_φ$ to be bounded from below on the pluriharmonic $α$-Bloch space $\mathcal{B}_{P(n,α)}$.
Source: arXiv (Cornell University)
Authors: Ahamed, Molla Basir, Allu, Vasudevarao
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221566195