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Lebesgue points of functions in the complex Sobolev space

Gabriel Vigny

https://orcid.org/0000-0002-4926-9794

LAMFA, Université de Picardie Jules Verne, 33 rue Saint-Leu, 80039 AMIENS Cedex 1, France

E-mail Address: gabriel.vigny@u-picardie.fr

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and

Duc-Viet Vu

https://orcid.org/0000-0002-0532-4966

Department of Mathematics and Computer Sciences, University of Cologne, Cologne, Germany

E-mail Address: dvu@uni-koeln.de

Corresponding author.

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https://doi.org/10.1142/S0129167X24500149Cited by:0 (Source: Crossref)

Abstract

Let $φ$ $φ$ be a function in the complex Sobolev space $W^{*} (U)$ $W^{*} (U)$ , where $U$ $U$ is an open subset in $ℂ^{k}$ . 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.

Communicated by Xiaonan Ma

Keywords:

AMSC: 32U05, 32U25, 32U40, 37F10

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