Approximation by weighted means of Walsh-Fourier series - F. Móricz; B. E. Rhoades (International Journal of Mathematics and Mathematical Sciences)
We study the rate of approximation to functions in Lp and, in particular, in Lip(α,p) by weighted means of their Walsh-Fourier series, where α>0 and 1≤p≤∞. For the case p=∞, Lp is interpreted to be CW, the collection of uniformly W continuous functions over the unit interval [0,1). We also note that the weighted mean kernel is quasi-positive, under fairly general conditions.