Solvability of the Gleason Problem on a Class of Bounded Pseudoconvex Domains
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DOI: 10.1007/s11785-022-01236-5
Abstract: A BSTRACT . We show that if a bounded pseudoconvex domain satisfies the solvability of the bounded ∂ problem, then the ideal of bounded holomorphic functions vanishing at a point α in the domain is… read more here.
Keywords: pseudoconvex; pseudoconvex domains; solvability gleason; gleason problem ... See more keywords
Gradients of inner functions in strictly pseudoconvex domains
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DOI: 10.1007/s11856-018-1777-y
Abstract: Assume that Ω is a bounded strictly pseudoconvex domain with C2 boundary. We prove the existence of a nonconstant inner function on Ω with gradient in L1(Ω). read more here.
Keywords: gradients inner; pseudoconvex domains; functions strictly; inner functions ... See more keywords
Estimates of Kähler-Einstein metrics on pseudoconvex domains of finite type with locally diagonalizable Levi form
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DOI: 10.1016/j.jmaa.2020.124644
Abstract: Abstract In this short note, we use the weights introduced by Ph. Charpentier and Y. Dupain on pseudoconvex domains of finite type with locally diagonalizable Levi form to prove that on these domains, the Kahler-Einstein… read more here.
Keywords: domains finite; pseudoconvex domains; locally diagonalizable; type locally ... See more keywords
The umbilical locus on the boundary of strictly pseudoconvex domains in ℂ2
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DOI: 10.1142/s0129167x17400018
Abstract: The main objective of this paper is to survey some recent results on the Chern–Moser question concerning existence of umbilical points on three-dimensional CR submanifolds in ℂ2. read more here.
Keywords: umbilical locus; locus boundary; pseudoconvex domains; strictly pseudoconvex ... See more keywords
The L2 ∂¯-cauchy problem on pseudoconvex domains and applications
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DOI: 10.1142/s1793557118500250
Abstract: Let X be a complex manifold of dimension n ≥ 2 and Ω ⋐ X be a weakly pseudoconvex domain with smooth boundary in X. Let E be a holomorphic line bundle over X which… read more here.
Keywords: cauchy problem; pseudoconvex domains; domains applications; problem pseudoconvex ... See more keywords
On some new sharp embedding theorems for multifunctional Herz-type and Bergman-type spaces in pseudoconvex domains
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DOI: 10.2298/fil1917677s
Abstract: We introduce new multifunctional mixed norm analytic Herz-type spaces in strongly pseudoconvex domains and provide new sharp embedding theorems for them. Some results are new even in case of onefunctional holomorphic spaces. Some new related… read more here.
Keywords: type spaces; pseudoconvex domains; herz type; type ... See more keywords