Q-effectiveness for holomorphic subelliptic multipliers

TL;DR

This paper solves the effectiveness problem in Kohn's algorithm for generating holomorphic subelliptic multipliers on special domains, leading to controlled subelliptic estimates for $(0,q)$ forms.

Contribution

It introduces a solution to the effectiveness problem in Kohn's algorithm for all $q$, enabling explicit subelliptic estimates on special domains.

Findings

Effective subelliptic estimates for $(0,q)$ forms with controlled Sobolev exponent

Solution to the effectiveness problem in Kohn's algorithm for arbitrary $q$

Application to domains defined by sums of squares of holomorphic functions

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 an application, we obtain subelliptic estimates for $(0,q)$ forms with effectively controlled order $\epsilon>0$ (the Sobolev exponent) for domains given by sums of squares of holomorphic functions (J.J. Kohn called them "special domains"). These domains are of particular interest due to their relation with complex and algebraic geometry. Our methods include triangular resolutions introduced by the authors in their previous work.