(untitled) (European Journal of Pure and Applied Mathematics, 2018)
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 Littlewood-Paley theory.