Acta mathematica scientia,Series B ›› 2024, Vol. 44 ›› Issue (2): 431-444.doi: 10.1007/s10473-024-0203-2

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ON THE SOBOLEV DOLBEAULT COHOMOLOGY OF A DOMAIN WITH PSEUDOCONCAVE BOUNDARIES

Jian CHEN   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2022-12-26 Revised:2023-05-22 Online:2024-04-25 Published:2023-12-06
  • About author:Jian CHEN, E-mail: jian-chen@whu.edu.cn

Abstract: 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¯mj=1Ωj, where ˜Ω and {Ωj}mj=1˜Ω are bounded pseudoconvex domains in Cn with smooth boundaries, and ¯Ω1,,¯Ωm are mutually disjoint. The main results can also be quickly obtained by virtue of [5].

Key words: Cauchy-Riemann equations, pseudoconcave domains, ˉ-Neumann operator, Bergman spaces

CLC Number: 

  • 32W05
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