# zbMATH — the first resource for mathematics

Inégalités $$L^ 2$$ et représentations de groupes nilpotents. ($$L^ 2$$-inequalities and representations of nilpotent groups). (French) Zbl 0644.35026
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

##### MSC:
 35H10 Hypoelliptic equations 58J10 Differential complexes 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
Full Text:
##### References:
 [1] Egorov, Y.V; Egorov, Y.V, Subelliptic operators, Russian math. surveys, Russian math. surveys, 30, No. 2, 55-105, (1975), No. · Zbl 0331.35054 [2] Helffer, B; Nourrigat, J; Helffer, B; Nourrigat, J, Caractérisation des opérateurs hypoelliptiques homogènes invariants à gauche sur un groupe nilpotent gradué, Comm. partial différential equations, Comm. partial différential equations, 4, No. 8, 899-958, (1979), No. · Zbl 0423.35040 [3] Helffer, B; Nourrigat, J, Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs, () · Zbl 0549.35026 [4] Hörmander, L, Subelliptic operators, () · 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 [7] {\scA. Melin}, Parametrix constructions for some classes of right invariant differential operators on nilpotent groups, Global Anal. Geom. paraître. · Zbl 0524.58044 [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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.