On the Sobolev Dolbeault cohomology of a domain with pseudoconcave boundaries

In this note, we mainly make use of a method devised by Shaw [15] for studying Sobolev Dolbeault cohomologies of a pseudoconcave domain of the type Ω = Ω ˜ \ ∪ j = 1 m Ω j ¯ , where Ω ˜ and { Ω j } j = 1 m ⋐ Ω ~ are bounded pseudoconvex domains in ℂ n with smooth boundaries, and Ω ¯ 1 , ⋯ , Ω ¯ m ar...

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Bibliographic Details
Published inActa mathematica scientia Vol. 44; no. 2; pp. 431 - 444
Main Author Chen, Jian
Format Journal Article
LanguageEnglish
Published Singapore Springer Nature Singapore 01.03.2024
Subjects
Analysis
Mathematics
Mathematics and Statistics
32A36
Neumann operator
35N15
Bergman spaces
32W05
Cauchy-Riemann equations
pseudoconcave domains
(?)-Neumann operator
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Summary:In this note, we mainly make use of a method devised by Shaw [15] for studying Sobolev Dolbeault cohomologies of a pseudoconcave domain of the type Ω = Ω ˜ \ ∪ j = 1 m Ω j ¯ , where Ω ˜ and { Ω j } j = 1 m ⋐ Ω ~ are bounded pseudoconvex domains in ℂ n with smooth boundaries, and Ω ¯ 1 , ⋯ , Ω ¯ m are mutually disjoint. The main results can also be quickly obtained by virtue of [5].
ISSN:0252-9602
1572-9087
DOI:10.1007/s10473-024-0203-2