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

abstract

• 2014, Springer-Verlag Berlin Heidelberg. Let $$M$$M be a pseudoconvex, oriented, bounded and closed CR submanifold of Cn of hypersurface type. Our main result says that when a certain 1-form on M is exact on the null space of the Levi form, then the complex Green operator on M satisfies Sobolev estimates. This happens in particular when M admits a set of plurisubharmonic defining functions or when M is strictly pseudoconvex except for the points on a simply connected complex submanifold.

authors

• Straube, Emil

published proceedings

• INVENTIONES MATHEMATICAE

author list (cited authors)

• Straube, E. J., & Zeytuncu, Y. E.

citation count

• 6

complete list of authors

• Straube, Emil J||Zeytuncu, Yunus E

publication date

• September 2015

publisher

• Springer Nature  Publisher

published in

• Inventiones Mathematicae  Journal

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics
• 4902 Mathematical Physics
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.1007/s00222-014-0564-6

start page

• 1073

end page

• 1095

volume

• 201

issue

• 3

URL

• http://dx.doi.org/10.1007/s00222-014-0564-6