De Rham cohomology of manifolds containing the points of infinite type, and Sobolev estimates for the problem Academic Article uri icon

abstract

  • We consider smooth bounded pseudoconvex domains Ω in Cn whose boundary points of infinite type are contained in a smooth submanifold M (with or without boundary) of the boundary having its (real) tangent space at each point contained in the null space of the Levi form of bΩ at the point. (In particular, complex submanifolds satisfy this condition.) We consider a certain one-form α on bΩ and show that it represents a De Rham cohomology class on submanifolds of the kind described. We prove that if α represents the trivial cohomology class on M, then the Bergman projection and the {Mathematical expression} operator on Ω are continuous in Sobolev norms. This happens, in particular, if M has trivial first De Rham cohomology, for instance, if M is simply connected. © 1993 Mathematica Josephina, Inc.

author list (cited authors)

  • Boas, H. P., & Straube, E. J.

citation count

  • 21

publication date

  • May 1993