On the Sobolev Dolbeault cohomology of a domain with pseudoconcave boundaries

• Published in: Acta mathematica scientia Vol. 44; no. 2; pp. 431 - 444
• Main Author: Chen, Jian
• Format: Journal Article
• Language: English
• 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

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...