Division and extension in weighted Bergman-Sobolev spaces.

Ortega, Joaquín M., and Fàbrega, Joan. "Division and extension in weighted Bergman-Sobolev spaces.." Publicacions Matemàtiques 36.2B (1992): 837-859. <http://eudml.org/doc/41756>.

@article{Ortega1992,
abstract = {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.},
author = {Ortega, Joaquín M., Fàbrega, Joan},
journal = {Publicacions Matemàtiques},
keywords = {division; weighted Bergman-Sobolev spaces; extension},
language = {eng},
number = {2B},
pages = {837-859},
title = {Division and extension in weighted Bergman-Sobolev spaces.},
url = {http://eudml.org/doc/41756},
volume = {36},
year = {1992},
}

TY - JOUR
AU - Ortega, Joaquín M.
AU - Fàbrega, Joan
TI - Division and extension in weighted Bergman-Sobolev spaces.
JO - Publicacions Matemàtiques
PY - 1992
VL - 36
IS - 2B
SP - 837
EP - 859
AB - 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.
LA - eng
KW - division; weighted Bergman-Sobolev spaces; extension
UR - http://eudml.org/doc/41756
ER -