Document type
ArticleVersion
Published versionPublication date
All rights reserved
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/132716
Division and extension in weighted Bergman-Sobolev spaces
Journal Title
Director/Tutor
Journal ISSN
Volume Title
Related resource
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.
Subject
Subject (English)
Citation
Citation
ORTEGA ARAMBURU, Joaquín M. and FÀBREGA CASAMITJANA, Joan. Division and extension in weighted Bergman-Sobolev spaces. Publicacions Matemàtiques. 1992. Vol. 36, num. 2, pags. 837-859. ISSN 0214-1493. [consulted: 7 of June of 2026]. Available at: https://hdl.handle.net/2445/132716