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arXiv · 2403.03568

Equivalence between VMO functions and plurisubharmonic functions with zero Lelong numbers

Séverine Biard·Jujie Wu
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Abstract

We prove that a plurisubharmonic function on a domain in the complex Euclidean space is a locally VMO (Vanishing Mean Oscillation) function if and only if its Lelong number at each point vanishes. We also give a global version of this result when the boundary of the domain satisfies the \textit{interior sphere condition}. An example emphasizes the importance of this condition. These equivalences contribute to a better understanding of the behavior of singular plurisubharmonic functions. We end the paper by discussing the link between the residual Monge-Amp\`ere mass and VMO functions, by providing examples.

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Séverine Biard, Jujie Wu. 2024-03-06. Equivalence between VMO functions and plurisubharmonic functions with zero Lelong numbers. https://arxiv.org/abs/2403.03568

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