Cohomology with \(L^ p\)-bounds on polycylinders (Q1895271)
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scientific article; zbMATH DE number 785302
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Cohomology with \(L^ p\)-bounds on polycylinders |
scientific article; zbMATH DE number 785302 |
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Cohomology with \(L^ p\)-bounds on polycylinders (English)
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15 August 1995
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If \(\Omega\) is a bounded polycylinder in \(\mathbb{C}^n\) and \(B_p\) denotes the sheaf of (germs of) \(L^p\)-holomorphic functions on \(\overline \Omega\), the authors prove that \(H^q (\overline \Omega, B_p) = 0\) for \(q \geq 1\). The proof makes use of a Dolbeault- Grothendieck lemma with \(L^p\)-bounds. As consequences of this result, the solvability of the weak Corona problem and a Leray's isomorphism theorem are also established.
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sheaf cohomology
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\(L^ p\)-bound-equation
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