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

Zheng Fang, Jianxun He

Abstract

In this paper, we consider Radon transform on the Heisenberg group $\textbf{H}^{n}$, 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 $L^{2}(\textbf{H}^{n})$. 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

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