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

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.

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