The angular distribution of mass by Bergman functions

  • Donald E. Marshall

    University of Washington, Seattle, USA
  • Wayne Smith

    University of Hawai‘i at Mānoa, Honolulu, USA


Let be the unit disk in the complex plane and denote by two-dimensional Lebesgue measure on . For we define arg . We prove that for every there exists a such that if is analytic, univalent and area-integrable on , and , then

. This problem arose in connection with a characterization by Hamilton, Reich and Strebel of extremal dilatations for quasiconformal homeomorphisms of .

Cite this article

Donald E. Marshall, Wayne Smith, The angular distribution of mass by Bergman functions. Rev. Mat. Iberoam. 15 (1999), no. 1, pp. 93–116

DOI 10.4171/RMI/251