Título inglés | Calderón's problem for Lipschitz classes and the dimension of quasicircles. |
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Título español | Problema de Calderón para clases de Lipschitz y la dimensión de cuasicírculos. |
Autor/es | Astala, Kari |
Organización | Dep. Math. Univ. Helsinki, Helsinki, Finlandia |
Revista | 0213-2230 |
Publicación | 1988, 4 (3-4): 469-486, 17 Ref. |
Tipo de documento | articulo |
Idioma | Inglés |
Resumen inglés | In the last years the mapping properties of the Cauchy integral CΓf(z) = 1/(2πi) ∫Γ [f(ξ) / ξ - z] dξ have been widely studied. The most important question in this area was Calderón's problem, to determine those rectifiable Jordan curves Γ for which CΓ defines a bounded operator on L2(Γ). The question was solved by Guy David [Da] who proved that CΓ is bounded on L2(Γ) (or on Lp(Γ), 1 < p < ∞) if and only if Γ is regular, i.e., H1(Γ ∩ B(z0,R) ≤ CR for every z0 Î C, R > 0 and for some constant C (...). |
Clasificación UNESCO | 120209 |
Palabras clave español | Integrales singulares ; Integral de Cauchy ; Dominios de Lipschitz |
Código MathReviews | MR1048585 |
Código Z-Math | Zbl 0703.30036 |
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