Nourrigat, Jean Inégalités \(L^ 2\) et représentations de groupes nilpotents. (\(L^ 2\)-inequalities and representations of nilpotent groups). (French) Zbl 0644.35026 J. Funct. Anal. 74, 300-327 (1987). The author extends the method of the proof for \(L^ 2\)-inequalities by means of the Fourier transform for operators with constant coefficients to the classes of hypoelliptic operators which are images in the representation of the nilpotent group G of left-invariant operators. Reviewer: S.Eloshvili Cited in 1 ReviewCited in 7 Documents MSC: 35H10 Hypoelliptic equations 58J10 Differential complexes 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods Keywords:Fourier transform for operators; constant coefficients; hypoelliptic operators; left-invariant operators × Cite Format Result Cite Review PDF Full Text: DOI Numdam References: [1] Egorov, Y. V., Subelliptic operators, Russian Math. Surveys, 30, 55-105 (1975), No. · Zbl 0331.35054 [2] Helffer, B.; Nourrigat, J., Caractérisation des opérateurs hypoelliptiques homogènes invariants à gauche sur un groupe nilpotent gradué, Comm. Partial Différential Equations, 4, 899-958 (1979), No. · Zbl 0423.35040 [3] Helffer, B.; Nourrigat, J., Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs, (Progress in Mathematics, Vol. 58 (1985), Birkhauser-Verlag: Birkhauser-Verlag Bâle) · Zbl 0549.35026 [4] Hörmander, L., Subelliptic operators, (Seminar on singularities of solutions of linear partial differential equations. Seminar on singularities of solutions of linear partial differential equations, Annals of Mathematical Studies, Vol. 91 (1978), Princeton Univ. Press: Princeton Univ. Press Princeton, N.J) · Zbl 0446.35086 [5] Hörmander, L., The Weyl calculus for pseudo-differential operators, Comm. Pure Appl. Math., 32, 359-443 (1979) · Zbl 0388.47032 [6] Kirillov, A., Unitary representations of nilpotent groups, Russian Math. Surveys, 17, 53-104 (1952) · Zbl 0106.25001 [8] Moukadem, N., Interpolation pour des espaces de Sobolev associés à des représentations de groupes nilpotents, Thèse de 3ème Cycle (1981), Rennes [9] Nourrigat, J., Réduction microlocale des systèmes d’opérateurs pseudodifférentiels (1984), préprint · Zbl 0543.35106 [10] Rockland, C., Hypoellipticity on the Heisenberg group, représentation theoretic criteria, Trans. Amer. Math. Soc., 240, 517, 1-52 (1978) · Zbl 0326.22007 [11] Rothschild, L. P.; Stein, E. M., Hypoelliptic differential operators and nilpotent groups, Acta Math., 137, 248-315 (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.