A note on degree of approximation by Nörlund and Riesz operators. (English) Zbl 0725.42004

The author proves that without the condition \(tH(t)=o(1)\) \((t\to 0+)\), he used in a previous proof to get the approximation \[ (*)\quad \| N_ n(f)-f\|_ p=O\{(p_ n/P_ n)H(p_ n/P_ n)\},\quad n\to \infty, \] the same order of approximation can be achieved. Similar result holds with Riesz means of Fourier series instead of the Nörlund means being in (*).


42A10 Trigonometric approximation