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

Abstract

A necessary and sufficient condition for regularity of the\(\bar \partial\)-Neumann operator on (0,q)-forms in a smooth bounded pseudoconvex domain in Cn is that the orthogonal projections onto\(\bar \partial\)-closed forms of degrees (0,q−1), (0,q), and (0,q+1) all be regular.