Compactness Estimate for the $\overline{\partial}$-Neumann Problem on a $Q$-Pseudoconvex Domain in a Stein Manifold
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Authors: S. SABER AND A. ALAHMARI
DOI: 10.46793/KgJMat2304.627S
Abstract:
We consider a smoothly bounded q-pseudoconvex domain Ω in an n-dimensional Stein manifold X and suppose that the boundary bΩ of Ω satisfies (q − P) property, which is the natural variant of the classical P property. Then, one prove the compactness estimate for the ∂-Neumann operator Nr,s in the Sobolev k-space. Applications to the boundary global regularity for the ∂-Neumann operator Nr,s in the Sobolev k-space are given. Moreover, we prove the boundary global regularity of the ∂-operator on Ω.
Keywords:
Stein manifold, q-pseudoconvex domain, compactness estimate, ∂-operator, ∂-Neumann operator.
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