Pointwise convergence of Cesàro and Riesz means on certain function spaces

Abstract

Abstract. We consider a function space QA on the unit sphere of R 3 , which contains L log L log log log L, and prove the spherical harmonics expansions of functions in QA are summable a.e. with respect to the Cesàro means of the critical order 1/2. We also prove that a similar result holds for the BochnerRiesz means of multiple Fourier series of periodic functions on R d , d ≥ 2.