Hölder Continuity and Boundedness of Composition Operators on Pluriharmonic α-Bloch Spaces
Abstract
In this paper, we study the metric properties of pluriharmonic α-Bloch-type mappings f=h+g̅∈ℋ(𝔹n,ℂn) on the unit ball 𝔹n⊂ℂn. By synthesizing local real-part estimates with the subharmonicity of log(| det Dh(z) | + | det Dg(z) |) along hyperbolic geodesics, we establish a globalized non-trivial lower bound across the entire unit ball 𝔹n. Using this structural decay estimate, we prove that the invariant weight quantity Dfn,α(z) satisfies a global Hölder continuity estimate of order 1/n with respect to the Bergman metric β. Furthermore, we investigate composition operators Cφ(f)=f∘φ induced by holomorphic self-mappings φ∈𝒜(𝔹n,𝔹n). We establish both sharp sufficient and necessary sampling conditions for Cφ to be bounded from below on the pluriharmonic α-Bloch space ℬP(n,α).
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BibTeX
@misc{ahamed2026hölder,
title = {{Hölder Continuity and Boundedness of Composition Operators on Pluriharmonic $α$-Bloch Spaces}},
author = {Molla Basir Ahamed and Vasudevarao Allu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12487},
eprint = {2610.12487},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12487},
}
RIS
TY - UNPB
TI - Hölder Continuity and Boundedness of Composition Operators on Pluriharmonic α-Bloch Spaces
AU - Molla Basir Ahamed
AU - Vasudevarao Allu
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.12487
UR - https://arxiv.org/abs/2610.12487
AB - In this paper, we study the metric properties of pluriharmonic α-Bloch-type mappings f=h+g̅∈ℋ(𝔹^n,ℂ^n) on the unit ball 𝔹^n⊂ℂ^n. By synthesizing local real-part estimates with the subharmonicity of log(| det Dh(z) | + | det Dg(z) |) along hyperbolic geodesics, we establish a globalized non-trivial lower bound across the entire unit ball 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∘φ induced by holomorphic self-mappings φ∈𝒜(𝔹^n,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 ℬ_P(n,α).
ER -