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Hypoellipticity on the Heisenberg group. (English) Zbl 0407.58036


MSC:

58J70 Invariance and symmetry properties for PDEs on manifolds
58J99 Partial differential equations on manifolds; differential operators
22E30 Analysis on real and complex Lie groups
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods

Citations:

Zbl 0326.22007
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Full Text: DOI

References:

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[3] Beals, R., Characterization of pseudodifferential operators and applications, Duke Math. J., 44, 45-57 (1977) · Zbl 0353.35088
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[7] Folland, G., Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Mat., 13, 161-207 (1975) · Zbl 0312.35026
[8] Folland, G.; Stein, E., Estimates for the \(∂b\) complex and analysis on the Heisenberg group, Comm. Pure Appl. Math., 27, 429-522 (1974) · Zbl 0293.35012
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[10] Grusin, V., Math. USSR-Sb., 13, 155-185 (1971) · Zbl 0238.47038
[11] Helgason, S., Differential Geometry and Symmetric Spaces (1962), Academic Press: Academic Press New York · Zbl 0122.39901
[12] Hewitt, E.; Ross, K., (Abstract Harmonic Analysis, I (1963), Springer-Verlag: Springer-Verlag New York) · Zbl 0837.43002
[13] Hormander, L., Linear Partial Differential Operators (1963), Springer-Verlag: Springer-Verlag New York · Zbl 0171.06802
[14] Kirillov, A., Russian Math. Surveys, 17, 53-104 (1962) · Zbl 0106.25001
[15] Kohn, J., Pseudo-differential operators and hypoellipticity, (Proc. Symp. Pure Appl. Math., 23 (1973)), 61-69 · Zbl 0262.35007
[16] Rockland, C., Hypoellipticity on the Heisenberg group: representation-theoretic criteria, Trans. Amer. Math. Soc., 240, 1-52 (1978) · Zbl 0326.22007
[17] Seeley, R., Regularization of singular integral operators on compact manifolds, Amer. J. Math., 81, 265-275 (1961) · Zbl 0192.23503
[18] Seeley, R., Integro-differential operators on vector bundles, Appendix, Trans. Amer. Math. Soc., 117, 197-204 (1965) · Zbl 0135.37102
[19] Treves, F., Topological Vector Spaces, Distributions and Kernels (1967), Academic Press: Academic Press New York · Zbl 0171.10402
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