Sup-norm Estimates for ∂ in ℂ³

2019/09/09 by Dusty Grundmeier, Grundmeier, Dusty, Lars Simon +3
Mathematics · #32A26 #32T25 #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1909.04080

openalex publication_date 2019/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a method for proving sup-norm and Hölder estimates for ∂ on wide class of finite type pseudoconvex domains in ℂⁿ. A fundamental obstruction to proving sup-norm estimates is the possibility of singular complex curves with exceptionally high order of contact with the boundary. Our method handles this problem, and in ℂ³, we prove sup-norm and Hölder estimates for all bounded, pseudoconvex domains with real-analytic boundary.

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