Pure and Applied Mathematics Quarterly
Volume 18 (2022)
Special issue in honor of Joseph J. Kohn on the occasion of his 90th birthday
Guest Editors: J.E. Fornaess, Stanislaw Janeczko, Duong H. Phong, and Stephen S.T. Yau
$q$-effectiveness for holomorphic subelliptic multipliers
Pages: 617 – 637
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 subelliptic estimates for $(0, q)$ forms with effectively controlled order $\varepsilon \gt 0$ (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 relation with complex and algebraic geometry. Our methods include triangular resolutions introduced by the authors in [KZ20].
This work was supported by the Institute for Basic Science (IBS-R032-D1-2021-a00).
Received 6 May 2021
Accepted 29 December 2021
Published 13 May 2022