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Commutative subalgebra of \(L^1(G)\) associated with a subelliptic operator on a Lie group \(G\). (English) Zbl 0311.22010


MSC:

22E25 Nilpotent and solvable Lie groups
22D15 Group algebras of locally compact groups
43A80 Analysis on other specific Lie groups
46J20 Ideals, maximal ideals, boundaries
43A15 \(L^p\)-spaces and other function spaces on groups, semigroups, etc.
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References:

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[9] A. Korányi and S. Vági, Singular integrals on homogeneous spaces and some problems of classical analysis, Ann. Scuola Norm. Sup. Pisa (3) 25 (1971), 575 – 648 (1972).
[10] Edward Nelson, Analytic vectors, Ann. of Math. (2) 70 (1959), 572 – 615. · Zbl 0091.10704 · doi:10.2307/1970331
[11] Elias M. Stein, Topics in harmonic analysis related to the Littlewood-Paley theory., Annals of Mathematics Studies, No. 63, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1970. · Zbl 0193.10502
[12] E. M. Stein, Some problems in harmonic analysis suggested by symmetric spaces and semi-simple groups, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 173 – 189.
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