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\({\bar \partial}\)-problem on weakly \(q\)-convex domains. (English) Zbl 0714.32006
We deal with a class of domains that we call weakly q-convex. These domains are generalizations of pseudoconvex domains. We show that we can solve the \({\bar \partial}\)-equation on weakly-\(q\)-convex domains on \((p,r)\)-forms for \(r\geq q\). We also show that we can prove other statements related to \({\bar \partial}\) in weakly \(q\)-convex domains that are true in pseudoconvex domains.
Reviewer: L.-H.Ho

32F99 Geometric convexity in several complex variables
32T99 Pseudoconvex domains
32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
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