Lebesgue points of functions in the complex Sobolev space

2023/06/21 by Gabriel Vigny, Vigny, Gabriel, Duc‐Viet Vu +1
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2306.12332

openalex publication_date 2023/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let φ be a function in the complex Sobolev space W^*(U), where 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∈ [1,2) is locally bounded from above by a plurisubharmonic function.

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