Lp harmonic analysis on the heisenberg group

Abstract

In the setting of the results proved by R.S Strichartz in the paper ”Lp Harmonic Analysis and Radon transforms on the Heisenberg Group”, we study the Lp spectral theory of the operator (−L)(iT)−1 obtained from the functional calculus of the operators L (the sublaplacian on the Heisenberg group) and T = ∂/∂t. We develop Littlewood-Paley theory for this operator using its heat semigroup. By establishing the Lp boundedness of the corresponding Littlewood-Paley g-function we prove a stronger result that Abel sums of the spectral projections converge almost everywhere as an extension to the Lp spectral theorem by proved R.S Strichartz.