Transference for Banach Space Representations of Nilpotent Lie Groups. Part 2. Pedersen Multipliers

Abstract

We characterize twisted convolutions associated with the Pedersen transform for unitary irreducible representations of nilpotent Lie groups. For $$1\\le p<\\infty $$\n , we also prove the $$L^p$$\n -boundedness for the Pedersen $$L^p$$\n -multipliers in the case of unitary irreducible representations that are square-integrable modulo the center of the group under consideration, thus, generalizing an earlier result on Weyl multipliers associated to the pseudo-differential Weyl calculus.