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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

##### MSC:
 32F99 Geometric convexity in several complex variables 32T99 Pseudoconvex domains 32W05 $$\overline\partial$$ and $$\overline\partial$$-Neumann operators
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##### References:
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