Littlewood-Paley g-function and Radon Transform on the Heisenberg Group
DOI:
https://doi.org/10.29020/nybg.ejpam.v11i1.3175Keywords:
Heisenberg group, Little-wood Pelay $g$-function, Radon transformAbstract
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.Downloads
Published
2018-01-30
Issue
Section
Functional Analysis
License
Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.
European Journal of Pure and Applied Mathematics will be Copyright Holder.
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