Ondelettes et intégrale de Cauchy sur les courbes lipschitziennes


We give a new real-variable proof of the $L^2$-boundedness of the Cauchy integral on Lipschitz curves, by constructing appropriate bases of wavelets on $L^2(\mathbf{R})$. What is new is the role played by the so-called multiscale analysis, and especially the notion of orthogonality.


Philippe Tchamitchian