Some remarks on Bochner-Riesz means

Abstract

We study L^p norm convergence of Bochner-Riesz means S^δ_Rƒ associated with certain non-negative differential operators. When the kernel S^m_R (x, y) satisfies a weak estimate for large values of m we prove L^p norm convergence of S^δ _Rƒ for δ > n|1/p-1/2|, 1 < p < ∞, where n is the dimension of the underlying manifold.