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

Authors

  • Zheng Fang
  • Jianxun He School of Mathematics and Information Sciences, Guangzhou University

DOI:

https://doi.org/10.29020/nybg.ejpam.v11i1.3175

Keywords:

Heisenberg group, Little-wood Pelay $g$-function, Radon transform

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.

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Published

2018-01-30

Issue

Vol. 11 No. 1: (January 2018)

Section

Functional Analysis

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How to Cite

Littlewood-Paley g-function and Radon Transform on the Heisenberg Group. (2018). European Journal of Pure and Applied Mathematics, 11(1), 138-149. https://doi.org/10.29020/nybg.ejpam.v11i1.3175