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A Characterization of Pluriharmonic Functions via p-Bergman Kernels and A Forelli-type Result
Abstract
Given a plurisubharmonic function φ>−∞ on the unit ball 𝔹n and a constant 0<p≤2, Guan-Zhou's optimal Lp extension theorem yields a sharp lower bound for the weighted p-Bergman kernel. We show that the equality holds at some point if and only if φ is pluriharmonic on 𝔹n. This provides an analogue of the equality part of Suita's conjecture. As an application, we prove a Forelli-type result. Let φ be a real-valued function on 𝔹n. If every slice of φ through the origin is harmonic and if φ is plurisubharmonic in a neighborhood of the origin, then φ is pluriharmonic on 𝔹n.
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BibTeX
@misc{xu2026characterization,
title = {{A Characterization of Pluriharmonic Functions via $p$-Bergman Kernels and A Forelli-type Result}},
author = {Wang Xu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32402},
eprint = {2609.32402},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32402},
}
RIS
TY - UNPB
TI - A Characterization of Pluriharmonic Functions via p-Bergman Kernels and A Forelli-type Result
AU - Wang Xu
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32402
UR - https://arxiv.org/abs/2609.32402
AB - Given a plurisubharmonic function φ>−∞ on the unit ball 𝔹^n and a constant 0<p≤2, Guan-Zhou's optimal L^p extension theorem yields a sharp lower bound for the weighted p-Bergman kernel. We show that the equality holds at some point if and only if φ is pluriharmonic on 𝔹^n. This provides an analogue of the equality part of Suita's conjecture. As an application, we prove a Forelli-type result. Let φ be a real-valued function on 𝔹^n. If every slice of φ through the origin is harmonic and if φ is plurisubharmonic in a neighborhood of the origin, then φ is pluriharmonic on 𝔹^n.
ER -