A characterization of right translation invariant operators from L ^P(Hⁿ, A) into L^q(Hⁿ, A)

Let Hn denote the Heisenberg group. In this paper, it is shown that if A is a commutative Banach algebra with a bounded approximate identity such that A* and A** have wide Radon Nikodym property, then there is an isometric isomorphism of the class of right translation invariant operators from Lp(Hn, A) into Lq(Hn, A**) onto the dual space of a certain function space where 1 < p, q < ∞. © SAS International Publications.