Lebesgue points of functions in the complex Sobolev space
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929243865219072 |
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| author | Vigny, Gabriel Vu, Duc-Viet |
| author_facet | Vigny, Gabriel Vu, Duc-Viet |
| contents | Let $φ$ be a function in the complex Sobolev space $W^*(U)$, where $U$ is an open subset in $\mathbb{C}^k$. We show that the complement of the set of Lebesgue points of $φ$ is pluripolar. The key ingredient in our approach is to show that $|φ|^α$ for $α\in [1,2)$ is locally bounded from above by a plurisubharmonic function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_12332 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lebesgue points of functions in the complex Sobolev space Vigny, Gabriel Vu, Duc-Viet Complex Variables Analysis of PDEs Let $φ$ be a function in the complex Sobolev space $W^*(U)$, where $U$ is an open subset in $\mathbb{C}^k$. We show that the complement of the set of Lebesgue points of $φ$ is pluripolar. The key ingredient in our approach is to show that $|φ|^α$ for $α\in [1,2)$ is locally bounded from above by a plurisubharmonic function. |
| title | Lebesgue points of functions in the complex Sobolev space |
| topic | Complex Variables Analysis of PDEs |
| url | https://arxiv.org/abs/2306.12332 |