Emil J. Straube

Equivalence of regularity for the Bergman projection and the\(\bar \partial\)-neumann operator

AbstractA necessary and sufficient condition for regularity of the

On equality of line type and variety type of real hypersurfaces in Cn

\bar \partial

Sobolev estimates for the complex green operator on a class of weakly pseudoconvex boundaries

-Neumann operator on (0,q)-forms in a smooth bounded pseudoconvex domain in Cn is that the orthogonal projections onto

Integral inequalities of Hardy and Poincaré type

\bar \partial

The Bergman projection on Hartogs domains in

-closed forms of degrees (0,q−1), (0,q), and (0,q+1) all be regular.

De Rham cohomology of manifolds containing the points of infinite type, and Sobolev estimates for the\(\bar \partial - Neumann\) problem

We show how to compute the Bergman kernel functions of some special domains in a simple way. As an application of the explicit formulas, we show that the Bergman kernel functions of some convex domains, for instance the domain in C^3 defined by the inequality |z_1|+|z_2|+|z_3|<1, have zeroes.