Nourrigat, J. Subelliptic systems. (English) Zbl 0723.35089 Commun. Partial Differ. Equations 15, No. 3, 341-405 (1990). The author studies a system of 2p first order pseudo-differential operators \(X_ j(\lambda)\), \(j=1,...,2p\), depending on a parameter \(\lambda >1\). Setting \(L_ j(\lambda)=X_ j(\lambda)+iX_{p+j}(\lambda)\), \(j=1,...,p\), he obtains a necessary and sufficient condition for the estimate \[ \sum^{2p}_{j=1}\| X_ j(\lambda)f\|^ 2\leq C\sum^{p}_{j=1}\| L_ j(\lambda)f\|^ 2,\quad \forall f\in S'({\mathbb{R}}^ d), \] provided \(\lambda\) is a large parameter. The proof is based on a careful and deep analysis of some model operators for which the author uses some general previous results concerning nilpotent groups and described in the book “Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs” (1985; Zbl 0568.35003) written jointly with B. Helffer. Some interesting applications for systems of subelliptic operators are given. Reviewer: V.Petkov (Bordeaux) Cited in 1 ReviewCited in 8 Documents MSC: 35S05 Pseudodifferential operators as generalizations of partial differential operators 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs Keywords:subelliptic operators Citations:Zbl 0568.35003 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Camus J., C.R.A.S. 283 pp 979– (1976) [2] DOI: 10.1080/03605308208820222 · Zbl 0497.35086 · doi:10.1080/03605308208820222 [3] DOI: 10.1070/RM1975v030n02ABEH001407 · Zbl 0318.35075 · doi:10.1070/RM1975v030n02ABEH001407 [4] DOI: 10.1002/cpa.3160340302 · Zbl 0458.35099 · doi:10.1002/cpa.3160340302 [5] Helffer B., C.R.A.S. 289 pp 775– (1979) [6] Helffer B., Progress in Math 58 [7] DOI: 10.2307/1970473 · Zbl 0132.07402 · doi:10.2307/1970473 [8] Hormander L., Ann. of Math. pp 127– (1979) [9] DOI: 10.1002/cpa.3160320304 · Zbl 0388.47032 · doi:10.1002/cpa.3160320304 [10] Hormander, L. 1985. ”The analysis of linear partial differential operators”. Springer. [11] DOI: 10.1070/RM1962v017n04ABEH004118 · Zbl 0106.25001 · doi:10.1070/RM1962v017n04ABEH004118 [12] Melin A., Preprint (1982) [13] Nourrigat J., Ann. Inst. Fourier 36 pp 83– (1986) · Zbl 0599.35140 · doi:10.5802/aif.1061 [14] J.Nourrigat Inegalites L2 et repr6sentations de groupes nilpotents. J. Funct.Analysis ,74 , 2 (1987) p.300-327. [15] J.Nourrigat Inegalites L2 et repr6sentations de groupes nilpotents. J. Funct.Analysis ,74 , 2 (1987) p.300-327. [16] J.Nourrigat Systbmes sous-elliptiques. Seminaire E.D.P. (Ecole Polytechnique), expos6 n05, 1986. [17] DOI: 10.1090/S0002-9947-1978-0486314-0 · doi:10.1090/S0002-9947-1978-0486314-0 [18] Rockland C., Preprint (1985) [19] Rothschild L. P., Acts MSth. 137 pp 248– (1977) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.