On Almost Everywhere Convergence of Bochner-Riesz Means in Higher Dimensions

In <!-- MATH ${{\mathbf{R}}^n}$ --> define <!-- MATH $({T_{\lambda ,r}}f)(\xi ) = \hat f(\xi )(1 - \left| {{r^{ - 1}}{\xi ^2}} \right|)_ + ^\lambda$ --> . If , <!-- MATH $\lambda > \tfrac{1}{2}(n - 1)/(n + 1)$ --> \tfrac{1}{2}(n - 1)/(n + 1)$"> and <!-- MATH $2 \leq p < 2n/(n - 1 - 2\lambda )$ --> <img width="219" height="41" align="MIDDLE" border="0" src="images/img7.gif" alt="$ 2 \leq p < 2n/(n - 1 - 2\lambda )$">, then <!-- MATH ${\lim _{r \to \infty }}{T_{\lambda ,r}}f(x) = f(x)$ --> a.e. for all <!-- MATH $f \in {L^p}({{\mathbf{R}}^n})$ --> .