Illinois Journal of Mathematics

Extension and restriction of holomorphic functions on convex finite type domains

M. Jasiczak

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Abstract

We consider holomorphic functions on a non-singular subvariety of a smoothly bounded convex domain of finite type. A sufficient and necessary condition is proved for such a function to have an extension to a $p$-integrable holomorphic function on the whole domain. This is shown under transversallity assumption and certain non-degeneracy condition of the subvariety.

Article information

Source
Illinois J. Math., Volume 54, Number 2 (2010), 509-542.

Dates
First available in Project Euclid: 14 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1318598671

Digital Object Identifier
doi:10.1215/ijm/1318598671

Mathematical Reviews number (MathSciNet)
MR2846472

Zentralblatt MATH identifier
1233.32005

Subjects
Primary: 32A35: Hp-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15] 32A36: Bergman spaces 32F32: Analytical consequences of geometric convexity (vanishing theorems, etc.) 32T25: Finite type domains 32T27: Geometric and analytic invariants on weakly pseudoconvex boundaries

Citation

Jasiczak, M. Extension and restriction of holomorphic functions on convex finite type domains. Illinois J. Math. 54 (2010), no. 2, 509--542. doi:10.1215/ijm/1318598671. https://projecteuclid.org/euclid.ijm/1318598671


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