Let D be a bounded strictly pseudoconvex domain of Cn with C ∞ 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 ∩ D. Also we give necessary and sufficient conditions on a set of holomorphic functions {fα}|α|≤m on M, so that there exists a holomorphic function in the Bergman-Sobolev space such that Dαf |M = fα for all |α| ≤ m.
@article{urn:eudml:doc:41756,
title = {Division and extension in weighted Bergman-Sobolev spaces.},
journal = {Publicacions Matem\`atiques},
volume = {36},
year = {1992},
pages = {837-859},
mrnumber = {MR1210023},
zbl = {0777.32004},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41756}
}
Ortega, Joaquín M.; Fàbrega, Joan. Division and extension in weighted Bergman-Sobolev spaces.. Publicacions Matemàtiques, Tome 36 (1992) pp. 837-859. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41756/