# Division and extension in weighted Bergman-Sobolev spaces.

Joaquín M. Ortega; Joan Fàbrega

Publicacions Matemàtiques (1992)

- Volume: 36, Issue: 2B, page 837-859
- ISSN: 0214-1493

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topOrtega, 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 -

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