Convergence rate of Cesaro means of Fourier-Laplace series

The convergence rate of Fourier-Laplace series in logarithmic subclasses of L-2(Sigma(d)) defined in terms of moduli of continuity is of interest. Lin and Wang [C. Lin, K. Wang, Convergence rate of Fourier-Laplace series of L-2-functions, J. Approx. Theory 128 (2004) 103-114] recently presented a characterization of those subclasses and provided the almost everywhere convergence rates of Fourier-Laplace series in those subclasses. In this note, the almost everywhere convergence rates of the Cesaro means for Fourier-Laplace series of the logarithmic subclasses are obtained. The strong approximation order of the Cesaro means and the partial summation operators are also presented. (c) 2006 Elsevier Inc. All rights reserved.