*(English)*Zbl 0856.42005

The reviewer observes that the statement of the given theorem is not complete since the conditions on $p$, $q$ and $\beta $ are missing. Also the authors claim to get an estimate for $|{\tilde{T}}_{n,p}-\tilde{f}|$ in ${L}_{p}$-norm which is really never used in the proof, where ${\tilde{T}}_{n,p}\left(x\right)$ are almost Nörlund means of the Fourier series of $f$ at $x$. In fact, they have tried to get an estimate for ${\tilde{T}}_{n,p}\left(x\right)-\tilde{f}\left(x\right)$ for all $x$ by assuming conditions, which seem to be in non-existence.

Surprisingly they assume $f\in W({L}^{p},{\psi}_{1}\left(t\right))$ but they mention on page 40, line 7, that $\psi \left(t\right)\in W({L}^{p},{\psi}_{1}\left(t\right))$, where $\psi \left(t\right)=f(x+t)-f(-t)$. Unfortunately whatever they have proved is also not correct since on page 40, lines 5-6 from bottom

Also the paper contains a number of misprints.

##### MSC:

42A10 | Trigonometric approximation |

41A25 | Rate of convergence, degree of approximation |

42A50 | Conjugate functions, conjugate series, singular integrals, one variable |