Subelliptic estimates for certain complexes of pseudodifferential operators (Q1094603)

The authors consider complexes of pseudodifferential operators of the form \[ u\to (P_ 1u,...,P_ ru),\quad (v_ 1,...,v_ r)\to (P_ iv_ j-P_ jv_ i)_{i<j}, \] etc., with \(P_ j=(\partial_{x_ j}+x_ j| D_ t|)I+N_ j(x,t,D_ t)\), where I is the identity matrix and \(N_ j\) is a matrix of pseudo-differential operators whose principal symbol \(N_ j(x,t,\lambda)\) is nilpotent. Results of subellipticity are proved, giving a more explicit version of the general necessary and sufficient condition of \textit{L. Hörmander} [Ann. Math., II. Ser. 83, 129-209 (1966; Zbl 0132.074)].