Pointwise convergence of Cesàro and Riesz means on certain function spaces

Abstract

We consider a function space QA on the unit sphere of R 3 , which contains LlogLlogloglogL, and prove the spherical harmonics expansions of functions in QA are summable a.e. with respect to the Cesaro means of the critical order 1/2. We also prove that a similar result holds for the Bochner- Riesz means of multiple Fourier series of periodic functions on R d , d � 2.