Inequalities of Brascamp-Lieb type on the Heisenberg group

Abstract

We prove both necessary and sufficient conditions for $L^p$-bound\-ed\-ness of certain multilinear generalized Radon transforms that arise as Heisenberg group analogues of the Brascamp--Lieb inequalities on Euclidean space. The necessary and sufficient conditions coincide in some important special cases, but differ in others.

We corrected the formulae of conditions (C1) and (C2), modified the statement of Proposition 2.2, and rewrote the proof of Lemma 4.4 for clarity; 13 pages