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Extension of holomorphic L 2-functions with weighted growth conditions

Published online by Cambridge University Press:  22 January 2016

Klas Diederich  and
Gregor Herbort
Klas Diederich
Affiliation:
Fachbereich Mathematik, Bergische Universität-Gesamthochschule Wuppertal Gauβstraβe20, D-56 Wuppertal
Gregor Herbort
Affiliation:
Fachbereich Mathematik, Bergische Universität-Gesamthochschule Wuppertal Gauβstraβe20, D-56 Wuppertal
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In this article a new contribution to the following question is given: Let Ω ⊂ ⊂ Cn be a bounded pseudoconvex domain with C∞-smooth boundary, q ∈ ∂Ω a fixed point and H a k-dimensional affine complex plane such that q ∈ H and H intersects ∂Ω at q transversally. Let U be a suitably small neighborhood of q, and denote by r a C∞-defining function of Ω on U. Under which conditions on ∂Ω near q is it possible to find an exponent η>0 > 0 such that every holomorphic function f on Ω′ = H ∩Ω∩ U with

where dλ′ denotes the Lebesgue-measure on H, can be extended to a holomorphic function ^f on Ω ∩ U such that even

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 126 , June 1992 , pp. 141 - 157
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1992

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