Resumen de The angular distribution of mass by Bergman functions

Donald E. Marshall, Wayne Smith

• Let D = {z: |z| < 1} be the unit disk in the complex plane and denote by dA two-dimensional Lebesgue measure on D. For e > 0 we define Se = {z: |arg z| < e}. We prove that for every e > 0 there exists a d > 0 such that if f is analytic, univalent and area-integrable on D, and f(0) = 0 then This problem arose in connection with a characterization by Hamilton, Reich and Strebel of extremal dilatation for quasiconformal homeomorphisms of D.