Abstract: | On bounded pseudoconvex domains Ω the orthogonal projection Pq : L2(p,q) (Ω) → ker q is given by Pq = Id – Sq+1 q = Id – *q+1Nq+1 q, where Sq is the canonical solution operator of the ‐equation and Nq is the ‐Neumann operator. We prove a formula for the solution operator Sq restricted on (0, q)‐forms with holomorphic coefficients. And as an application we get a characterization of compactness of the solution operator restricted on (0, q)‐forms with holomorphic coefficients. On general (0, q)‐forms we show that this condition is necessary for compactness of the solution operator. |