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Global solutions with \(C^k\)-estimates for bar-\(d\)-equations on \(q\)-concave intersections. (English) Zbl 1287.32002

Summary: We construct a global solution to the \(\bar{\partial}\)-equation with \(\mathcal{C}^k\)-estimates on \(q\)-concave intersections in \(\mathbb{C}^n\). Our main tools are integral formulas.

MSC:

32A26 Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels)
32F10 \(q\)-convexity, \(q\)-concavity
32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
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