Fejér's theorem for the classes \({\mathcal W}_ p\) (Q1092269)

The sequence of elements of a Fourier series of a function belonging to the Wiener class \({\mathcal W}_ p\), \(p>1\) (or to the Waterman class \(\{n^{\beta}\}BV\) or to the Chanturiya class \(V[n^{\beta}]\) for each \(0<\beta <1)\) is summable to \((f(x+0)-f(x-0))/\pi\) by the methods of Cesaro of order \(\alpha >1-1/p\) \((\alpha >\beta)\).