On the Rate of Almost Everywhere Convergence of Certain Classical Integral Means

AbstractThe main purpose of this article is to establish nearly optimal results concerning the rate of almost everywhere convergence of the Gauss–Weierstrass, Abel–Poisson, and Bochner–Riesz means of the one-dimensional Fourier integral. A typical result for these means is the following: If the function f belongs to the Besov spaceBsp,p, 1<p<∞, 0<s