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.