A division problem for\bar \partial _b - CLOSED forms |
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Authors: | Mats Andersson |
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Institution: | 1. Department of Mathematics, Chalmers University of Technology, S-41296, G?teborg, Sweden 2. University of G?teborg, S-41296, G?teborg, Sweden
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Abstract: | LetG
1,…,Gm be bounded holomorphic functions in a strictly pseudoconvex domainD such that
. We prove that for each
(0,q)-form ϕ inL
p(∂D), 1<p<∞, there are
formsu
1, …,u
m inL
p(∂D) such that ΣG
juj=ϕ. This generalizes previous results forq=0. The proof consists in delicate estimates of integral representation formulas of solutions and relies on a certainT1 theorem due to Christ and Journé. For (0,n−1)-forms there is a simpler proof that also gives the result forp=∞. Restricted to one variable this is precisely the corona theorem.
The author was partially supported by the Swedish Natural Research Council. |
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Keywords: | |
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