Complex analysis
Global regularity and Lp-estimates for ¯ on an annulus between two strictly pseudoconvex domains in a Stein manifold
Comptes Rendus. Mathématique, Volume 351 (2013) no. 23-24, pp. 883-888.

In this note, we prove an L2-existence theorem for the ¯-Neumann operator and the regularity for the ¯-equation on an annulus type domain D=D1D2¯, where D1 and D2 are strictly pseudoconvex domains with smooth boundaries in a Stein manifold X of complex dimension n3, such that D2¯D1X. Moreover, we obtain Hölder and Lp estimates for the ¯-equation on strictly pseudoconcave domains with smooth C3-boundaries in X.

Dans cette Note, nous démontrons un théorème dʼexistence L2 pour lʼopérateur de Neumann ¯ et la régularité globale au bord de lʼéquation ¯ sur de domaine de type couronne D=D1D¯2D1 et D2 sont des domaines strictement pseudo-convexes dont les bords sont réguliés dans une variété de Stein X de dimension complexe n3, tels que D¯2D1X. De plus, nous obtenons des estimations de Hölder et Lp, 1p, pour ¯ sur des domaines strictement pseudo-concaves de frontière C3 dans X.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2013.10.020
Khidr, Shaban 1; Abdelkader, Osama 2

1 Mathematics Department, Faculty of Science, King Abdelaziz University, North Jeddah, Jeddah, Saudi Arabia
2 Mathematics Department, Faculty of Science, El-minia University, El-minia, Egypt
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Khidr, Shaban; Abdelkader, Osama. Global regularity and $ {L}^{p}$-estimates for $ \overline{\partial }$ on an annulus between two strictly pseudoconvex domains in a Stein manifold. Comptes Rendus. Mathématique, Volume 351 (2013) no. 23-24, pp. 883-888. doi : 10.1016/j.crma.2013.10.020. http://www.numdam.org/articles/10.1016/j.crma.2013.10.020/

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