Birth and life of the $L^2$ boundedness of the Cauchy Integral on Lipschitz graphs

Abstract

We review various motives for considering the problem of estimating the Cauchy Singular Integral on Lipschitz graphs in the $L^2$ 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.

to appear in "Selected works of Yves Meyer", in the series "Documents mathématiques, Société Mathématique de France"

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