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arXiv · 2306.12332

Lebesgue points of functions in the complex Sobolev space

Gabriel Vigny·Duc-Viet Vu
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Abstract

Let $\varphi$ 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 $\varphi$ is pluripolar. The key ingredient in our approach is to show that $|\varphi|^\alpha $ for $\alpha \in [1,2)$ is locally bounded from above by a plurisubharmonic function.

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Gabriel Vigny, Duc-Viet Vu. 2023-06-21. Lebesgue points of functions in the complex Sobolev space. https://arxiv.org/abs/2306.12332

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