L^p-boundedness of the Bochner-Riesz operator

In this paper, we give a new approach to the Bochner-Riesz summability. As a result, we show that the Bochner-Riesz operator ${\mathbf{S}}^{\delta },0<\mathrm{\Re }\delta <\frac{1}{2}$ is bounded on ${\mathbf{L}}^p({\mathbb{R}}^n)$ for $\frac{n-1}{2n}\le \frac{1}{p}\le \frac{n+1}{2n}$.