Convergence rate of Cesàro means of Fourier–Laplace series

The convergence rate of Fourier–Laplace series in logarithmic subclasses of L2(Σd) defined in terms of moduli of continuity is of interest. Lin and Wang [C. Lin, K. Wang, Convergence rate of Fourier–Laplace series of L2-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 Cesàro means for Fourier–Laplace series of the logarithmic subclasses are obtained. The strong approximation order of the Cesàro means and the partial summation operators are also presented.