Division and extension in weighted Bergman-Sobolev spaces

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 functi...

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Detalles Bibliográficos
Autores: Ortega Aramburu, Joaquín M., Fàbrega Casamitjana, Joan
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:1992
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/132716
Acceso en línea:https://hdl.handle.net/2445/132716
Access Level:acceso abierto
Palabra clave:Espais de Sobolev
Anàlisi funcional
Sobolev spaces
Functional analysis
Descripción
Sumario: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.