Sobolev estimates for the complex Green operator on CR submanifolds of hypersurface type

• 成果类型: Article
• 署名作者: Straube, Emil J.; Zeytuncu, Yunus E.
• 署名单位: Texas A&M University System; Texas A&M University College Station; University of Michigan System; University of Michigan
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0564-6
• 发表日期: 2015
• 页码: 1073-1095
• 关键词: bergman projection; global regularity; partial-derivative(b); propagation; MANIFOLDS; domains

摘要

Let be a pseudoconvex, oriented, bounded and closed CR submanifold of of hypersurface type. Our main result says that when a certain -form on is exact on the null space of the Levi form, then the complex Green operator on satisfies Sobolev estimates. This happens in particular when admits a set of plurisubharmonic defining functions or when is strictly pseudoconvex except for the points on a simply connected complex submanifold.