Birth and life of the L² boundedness of the Cauchy Integral on Lipschitz graphs

2021/09/14 by Joan Verdera, Verdera, Joan · 2 citations
Mathematics · #31A15 (primary) #49K20 (secondary) #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2109.06690

openalex publication_date 2021/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We review various motives for considering the problem of estimating the Cauchy Singular Integral on Lipschitz graphs in the L² norm. We follow the thread that led to the solution and then describe a few of the innumerable applications and ramifications of this fundamental result. We concentrate on its influence in complex analysis, geometric measure theory and harmonic measure.

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