Littlewood-Paley g-function and Radon Transform on the Heisenberg Group (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.
Keywords: Heisenberg group; Little-wood Pelay $g$-function; Radon transform