Geodesic
The $\bar\partial$-Cauchy Problem on Weakly $q$-Convex Domains in $\Bbb{C}P^n$
Kragujevac Journal of Mathematics, Tome 44 (2020) no. 4, p. 581 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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Let $D$ be a weakly $q$-convex domain in the complex projective space $\Bbb{C}P^n$. In this paper, the (weighted) $\bar\partial$-Cauchy problem with support conditions in $D$ is studied. Specifically, the modified weight function method is used to study the $L^2$ existence theorem for the $\bar\partial$-Neumann problem on $D$. The solutions are used to study function theory on weakly $q$-convex domains via the $\bar\partial$-Cauchy problem.
Classification : 32F10 32W05
Keywords: $\bar\partial$, $\bar\partial$-Neumann operator, $q$-convex domains 
@article{KJM_2020_44_4_a8,
     author = {Sayed Saber},
     title = {The $\bar\partial${-Cauchy} {Problem} on {Weakly} $q${-Convex} {Domains} in $\Bbb{C}P^n$},
     journal = {Kragujevac Journal of Mathematics},
     pages = {581 },
     year = {2020},
     volume = {44},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2020_44_4_a8/}
}
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Sayed Saber. The $\bar\partial$-Cauchy Problem on Weakly $q$-Convex Domains in $\Bbb{C}P^n$. Kragujevac Journal of Mathematics, Tome 44 (2020) no. 4, p. 581 . http://geodesic.mathdoc.fr/item/KJM_2020_44_4_a8/