Integral representations of differential forms on Cauchy-Riemann manifolds and the theory of CR-functions

DOI10.1070/RM1984v039n03ABEH003163zbMath0589.32035OpenAlexW2099099333MaRDI QIDQ3717393

R. A. Airapetyan, Gennadi M. Henkin

Publication date: 1984

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/rm1984v039n03abeh003163

zbMATH Keywords

functionsintegralreal submanifolds of complex manifoldsdifferential forms on CR-manifoldsedge of the wedge theorems for CR-formsholomorphic extension of CRrepresentation formula of Cauchy-Fantappié type fortangential Cauchy-Riemann equations on q-concave manifolds

Mathematics Subject Classification ID

Continuation of analytic objects in several complex variables (32D15) Real submanifolds in complex manifolds (32V40) (q)-convexity, (q)-concavity (32F10) (overlinepartial) and (overlinepartial)-Neumann operators (32W05) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25)

Related Items (20)

On the removable singularities of CR functions given on a generic manifold ⋮ Some applications of Serre duality in CR manifolds ⋮ Global homotopy formulas on \(q\)-concave \(CR\) manifolds for large degrees ⋮ Distributional boundary values of holomorphic functions on product domains ⋮ Sharp estimates for the operator \(\overline{\partial}_M\) on a \(q\)-concave CR-manifold ⋮ Poincaré lemma and global homotopy formulas with sharp anisotropic Hölder estimates in \(q\)-concave CR manifolds ⋮ Conditions for holomorphic extendability of functions from borders of domains ⋮ Principe de Hartogs dans les variétés CR. (The Hartogs principle for CR manifolds) ⋮ Analysis of the Kohn Laplacian on quadratic CR manifolds. ⋮ Integral representation formulas for differential forms on complex manifolds and applications to the \({\bar \partial}\)-equation ⋮ Global homotopy formulas on \(q\)-concave CR manifolds for small degrees ⋮ Conormal suspensions of differential complexes ⋮ Unnamed Item ⋮ The tangential \(k\)-Cauchy-Fueter complexes and Hartogs' phenomenon over the right quaternionic Heisenberg group ⋮ Automorphisms and holomorphic mappings of standard CR-manifolds and Siegel domains ⋮ Global solution with \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$ \mathcal {C}^{k}$\end{document}-estimates for \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\bar{\partial }$\end{document}-eq ⋮ Optimal regularity for \(\overline\partial_b\) on CR manifolds ⋮ The relative Hartogs- Bochner phenomenon in a 2-concave real hypersurface in a complex analytic manifold ⋮ Sharp Lipschitz estimates for operator \(\overline\partial_ M\) on a \(q\)-pseudoconcave CR manifold. ⋮ Hypoellipticity in the tangential Cauchy-Riemann complex

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