Sobolev Estimates for the ∂ ¯ and the ∂ ¯ -Neumann Operator on Pseudoconvex Manifolds

Haroun Doud Soliman Adam, Khalid Ibrahim Adam Ahmed, Sayed Saber and Marin Marin ()
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Haroun Doud Soliman Adam: Department of Basic Sciences, Deanship of the Preparatory Year, Najran University, P.O. Box 1988, Najran 55461, Saudi Arabia
Khalid Ibrahim Adam Ahmed: Department of Basic Sciences, Deanship of the Preparatory Year, Najran University, P.O. Box 1988, Najran 55461, Saudi Arabia
Sayed Saber: Department of Mathematics and Statistics, Faculty of Science, Beni-Suef University, Beni-Suef 62511, Egypt
Marin Marin: Department of Mathematics and Computer Science, Transilvania University of Brasov, 500036 Brasov, Romania

Mathematics, 2023, vol. 11, issue 19, 1-26

Abstract: Let D be a relatively compact domain in an n -dimensional Kähler manifold with a C 2 smooth boundary that satisfies some “Hartogs-pseudoconvexity” condition. Assume that Ξ is a positive holomorphic line bundle over X whose curvature form Θ satisfies Θ ≥ C ω , where C > 0 . Then, the ∂ ¯ -Neumann operator N and the Bergman projection P are exactly regular in the Sobolev space W m ( D , Ξ ) for some m , as well as the operators ∂ ¯ N , ∂ ¯ ⋇ N .

Keywords: ? ¯; ? ¯ -Neumann operator; Kähler manifold; q-convex domain (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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