ON THEOREMS OF MORGAN AND COWLING-PRICE FOR SELECTED NILPOTENT LIE GROUPS

摘要

Let G be a connected, simply connected nilpotent Lie group. For p, q is an element of [1, +infinity], the L-p - L-q analogue of Morgan's theorem was proved only for two step nilpotent Lie groups. In order to study this problem in larger subclasses, we formulate and prove a version of L-p - L-q Morgan's theorem on nilpotent Lie groups whose Lie algebra admits an ideal which is a polarization for a dense subset of generic linear forms on the Lie algebra. A proof of an analogue of Cowling-Price Theorem is also provided in the same context.