$L^p$--Inequalities and Parseval-type relations for the index ${ }_2F_1 -$transform

Abstract

In this article the authors study $L^p$--boundedness properties for the index ${ }_2F_1 -$transform over the spaces $L_{\gamma ,p} \big(\mathbb{R}_{+} \big)$, $1\leq p < \infty$, $\gamma \in\mathbb{R}$, and $L^{\infty}\big(\mathbb{R}_{+}\big)$. Further, it is also obtained Parseval-type relations over these spaces.