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Hartogs theorem for forms: solvability of Cauchy-Riemann operator at critical degree. (English) Zbl 1170.32303
Summary: The Hartogs theorem for holomorphic functions is generalized in two settings: a CR version (Theorem 1.2) and a corresponding theorem based on it for \(C^k\) \(\overline\partial\)-closed forms at the critical degree, \(0 \leq k\leq\infty\) (Theorem 1.1). Part of Frenkel’s lemma in \(C^k\) category is also proved.
MSC:
32A26 Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels)
32W10 \(\overline\partial_b\) and \(\overline\partial_b\)-Neumann operators
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References:
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