Oscillating multipliers on the Heisenberg group

Abstract

Let L be the sublaplacian on the Heisenberg group Hⁿ. A recent result of Müller and Stein shows that the operator L-½ sin √L is bounded on L^p(Hⁿ) for all p satisfying |1/p-½|>1/(2n).In theis paper we show that the same operator is bounded on L^p in the bigger range |1/p-½|<1/2n-1)if we consider only functions which are band limited in the central variable.