q-effectiveness for holomorphic subelliptic multipliers

Abstract

We provide a solution to the effectiveness problem in Kohn’s algorithm for generating holomorphic subelliptic multipliers for (0, q) forms for arbitrary q. As application, we obtain subel-liptic estimates for (0, q) forms with effectively controlled order ε > 0 (the Sobolev exponent) for domains given by sums of squares of holomorphic functions (J.J. Kohn called them “special domains” in [K79]). These domains are of particular interest due to their re-lation with complex and algebraic geometry. Our methods include triangular resolutions introduced by the authors in [KZ20].