On the boundedness and unboundedness of certain convolution operators on nilpotent Lie groups
Proc. Amer. Math. Soc. 39 (1973), 409-413
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Abstract: One method of proving irreducibility of the ``principal series'' representations of semisimple Lie groups involves showing that a certain nonintegrable function on a nilpotent subgroup cannot be regularized to give a bounded convolution operator on . This note gives an elementary proof of this unboundedness property for the groups which occur in real-rank one semisimple groups.
H. Hardy, J.
E. Littlewood, and G.
Pólya, Inequalities, Cambridge, at the University
Press, 1952. 2d ed. MR
W. Knapp and E.
M. Stein, Intertwining operators for semisimple groups, Ann.
of Math. (2) 93 (1971), 489–578. MR
- G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, 2nd ed., Cambridge Univ. Press, New York, 1952. MR 13, 727. MR 0046395 (13:727e)
- A. W. Knapp and E. M. Stein, Intertwining operators for semi-simple groups, Ann. of Math. (2) 93 (1971), 489-578. MR 0460543 (57:536)
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