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 },
     publisher = {mathdoc},
     volume = {47},
     number = {4},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2023_47_4_a10/}
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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/