Some remarks on Bochner-Riesz means
Volume 83 / 2000
Colloquium Mathematicum 83 (2000), 217-230
DOI: 10.4064/cm-83-2-217-230
Abstract
We study norm convergence of Bochner-Riesz means S_R^δ f associated with certain non-negative differential operators. When the kernel S_R^m(x,y) satisfies a weak estimate for large values of m we prove L^p norm convergence of S_R^δ f for δ > n|1/p-1/2|, 1 < p < ∞, where n is the dimension of the underlying manifold.