Approximation properties of some means of Fourier series (Q1280027)

The author gives estimates for the rate of the approximation \(\|f- V_m[f]\|_p\) by the means \[ V_m[f](x):= \sum^m_{k= -m}\lambda \Biggl({k\over m+1}\Biggr) c_ke^{ikx}, \] where \(\lambda\) is a complex-valued function continuous on \((-\infty,\infty)\) and satisfies certain additional conditions. He considers both the cases \(0<p<1\) and \(p\geq 1\); and \(\|\cdot\|_p\) denotes the usual definition.