Geodesic
Compactness Estimate for the $\bar\partial$-Neumann Problem on a $Q$-Pseudoconvex Domain in a Stein Manifold
Kragujevac Journal of Mathematics, Tome 47 (2023) no. 4, p. 627 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

We consider a smoothly bounded $q$-pseudoconvex domain $\Omega$ in an $n$-dimensional Stein manifold $X$ and suppose that the boundary $b\Omega$ of $\Omega$ satisfies $(q-P)$ property, which is the natural variant of the classical $P$ property. Then, one prove the compactness estimate for the $\bar\partial$-Neumann operator $N_{r,s}$ in the Sobolev $k$-space. Applications to the boundary global regularity for the $\bar\partial$-Neumann operator $N_{r,s}$ in the Sobolev $k$-space are given. Moreover, we prove the boundary global regularity of the $\overline{\partial}$-operator on $\Omega$.
Classification : 32F10 32W05
Keywords: Stein manifold, $q$-pseudoconvex domain, compactness estimate, $\bar\partial$-operator, $\bar\partial$-Neumann operator 
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     author = {Sayed Saber and Abdullah Alahmari},
     title = {Compactness {Estimate} for the $\bar\partial${-Neumann} {Problem} on a $Q${-Pseudoconvex} {Domain} in a {Stein} {Manifold}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {627 },
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     volume = {47},
     number = {4},
     year = {2023},
     language = {en},
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Sayed Saber; Abdullah Alahmari. Compactness Estimate for the $\bar\partial$-Neumann Problem on a $Q$-Pseudoconvex Domain in a Stein Manifold. Kragujevac Journal of Mathematics, Tome 47 (2023) no. 4, p. 627 . http://geodesic.mathdoc.fr/item/KJM_2023_47_4_a10/