An Estimate for the Bochner-Riesz Operator on Functions of Product Type in $R^2$

Abstract

In this paper we shall give $L^p(\mathbf{R}^2)$-boundedness of the Bochner-Riesz operator $S_\delta$ for $2<p<\infty$ and $\delta>0$, restricting it to functions of product type. In this range, $2<p<\infty$ and $\delta>0$, the strong $L^p$-estimate is valid for functions of product type but not for general functions.