The angular distribution of mass by Bergman functions

• Autores: Donald E. Marshall, Wayne Smith
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 15, Nº 1, 1999, págs. 93-116
• Idioma: inglés
• DOI: 10.4171/rmi/251
• Títulos paralelos:
  • Distribución angular de masa por funciones de Bergman.
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• Resumen

  • 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.