Calderón's Problem for Lipschitz Classes and the Dimension of Quasicircles.

• Autores: Kari Astala
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 4, Nº 3-4, 1988, págs. 469-486
• Idioma: inglés
• Títulos paralelos:
  • Problema de Calderón para clases de Lipschitz y la dimensión de cuasicírculos.
• Enlaces
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• Resumen

  • In the last years the mapping properties of the Cauchy integral CGf(z) = 1/(2pi) ?G [f(?) / ? - z] d? have been widely studied. The most important question in this area was Calderón's problem, to determine those rectifiable Jordan curves G for which CG defines a bounded operator on L2(G). The question was solved by Guy David [Da] who proved that CG is bounded on L2(G) (or on Lp(G), 1 < p < 8) if and only if G is regular, i.e., H1(G n B(z0,R) = CR for every z0 Î C, R > 0 and for some constant C (...).