FOURIER SERIES ACCELERATION AND HARDY-LITTLEWOOD SERIES

We discuss the effects of the ${\delta}^2$ and Lubkin acceleration methods on the partial sums of Fourier Series. We construct continuous, even H$\ddot{o}$lder continuous functions, for which these acceleration methods fail to give convergence. The constructed functions include some interesting trigonometric series whose properties were investigated by Hardy and Littlewood.