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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.03568 |
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| _version_ | 1866912762709409792 |
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| author | Biard, Séverine Wu, Jujie |
| author_facet | Biard, Séverine Wu, Jujie |
| contents | 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-Ampère mass and VMO functions, by providing examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03568 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivalence between VMO functions and plurisubharmonic functions with zero Lelong numbers Biard, Séverine Wu, Jujie Complex Variables 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-Ampère mass and VMO functions, by providing examples. |
| title | Equivalence between VMO functions and plurisubharmonic functions with zero Lelong numbers |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2403.03568 |