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Title: Division and extension in weighted Bergman-Sobolev spaces
Author: Ortega Aramburu, Joaquín M.
Fàbrega Casamitjana, Joan
Keywords: Espais de Sobolev
Anàlisi funcional
Sobolev spaces
Functional analysis
Issue Date: 1992
Publisher: Universitat Autònoma de Barcelona
Abstract: 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.
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It is part of: Publicacions Matemàtiques, 1992, vol. 36, num. 2, p. 837-859
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ISSN: 0214-1493
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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