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Sobolev estimates for the Lewy operator on weakly pseudo-convex boundaries. (English) Zbl 0588.32023
The authors prove a regularity theorem, with optimal estimates in the Sobolev norm, for the global \({\bar \partial}_ b\) problem on forms of top degree on the boundary of smooth, pseudoconvex domain. The methods are a combination of integral formulas and weighted estimates.
The paper contains a detailed account of the history of this and related problems.
Reviewer: S.Krantz

MSC:
32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
35N15 \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs
32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
32T99 Pseudoconvex domains
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