La integral de Cauchy, capacitat analítica i aproximació

We intend to consider several problems related to One Complex Variable, Potential Theory and Singular integrals. 1. The Cauchy Integral: the goal is to describe in terms of curvature all positive measures for wich the Cautchy integral is bounded on L\super 2\sub \nosub \nosuper 2. Analytic capacity: we wish to prove that a set of finite length and Bercovitch irregular has zero analytic capacity. 3. Approximation: we propose to solve the problem of uniform approximation for the square of the Cauchy-Riemann operator