Littlewood-Paley g-function and Radon Transform on the Heisenberg Group

Abstract

Abstract. In this paper, we consider Radon transform on the Heisenberg group H n , and obtain new inversion formulas via dual Radon transforms and Poisson integrals. We prove that the Radon transform is a unitary operator from Sobelov space W into L 2 (H n ). Moreover, we use the Radon transform to define the Littlewood-Paley g-function on a hyperplane and obtain the LittlewoodPaley theory.2010 Mathematics Subject Classifications: 44A12; 43A15