Oscillating multipliers on the Heisenberg group
Volume 90 / 2001
Colloquium Mathematicum 90 (2001), 37-50
MSC: Primary 43A80, 43A22; Secondary 42C10, 22E30.
DOI: 10.4064/cm90-1-3
Abstract
Let ${\cal L} $ be the sublaplacian on the Heisenberg group $ H^n$. A recent result of Müller and Stein shows that the operator $ {{\cal L}}^{-1/2} \mathop {\rm sin}\nolimits \sqrt{{\cal L}} $ is bounded on $ L^p(H^n) $ for all $ p $ satisfying $ |1/p-1/2| < 1/(2n)$. In this paper we show that the same operator is bounded on $ L^p $ in the bigger range $ |1/p-1/2| < 1/(2n-1)$ if we consider only functions which are band limited in the central variable.
