On theorems of Morgan and Cowling-Price for selected nilpotent Lie groups

Abstract

Let G be a connected, simply connected nilpotent Lie group. For p,q ∈ [1,+∞] , the Lp −Lq 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 Lp − Lq 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. Mathematics subject classification (2010): Primary 22E25, Secondary 43A25.