Division and extension in weighted Bergman-Sobolev spaces

• Autores: Joan Fábrega, Joaquín María Ortega Aramburu
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 36, Nº 2, 2, 1992 (Ejemplar dedicado a: la memória de Pere Menal i Brufal), págs. 837-859
• Idioma: inglés
• DOI: 10.5565/publmat_362b92_08
• Títulos paralelos:
  • División y extensión en espacios de Bergman-Sobolev ponderados
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• Resumen

  • Let D be a bounded strictly pseudoconvex domain of Cn with C 8 boundary and Y = {z; u1(z) = ... = ul(z) = 0} a holomorphic submanifold in the neighbourhood of D', of codimension l and transversal to the boundary of D.

    In this work we give a decomposition formula f = u1f1 + ... + ulfl for functions f of the Bergman-Sobolev space vanishing on M = Y n D. Also we give necessary and sufficient conditions on a set of holomorphic functions {fa}|a|=m on M, so that there exists a holomorphic function in the Bergman-Sobolev space such that Daf |M = fa for all |a| = m.