The approximation of functions from LlogL(loglogL)(SN) by Fourier-Laplace series

In this paper, a study of the approximation of functions from LlogL(loglogL)(SN) by Fourier-Laplace series is performed. It is proved that the maximal operator of the Riesz means of the Fourier-Laplace series is bounded, from L1 to LlogL(loglogL)(SN). The result provides a natural and intrinsic characterization of the approximation of the functions by Fourier-Laplace series.