Pointwise strong and very strong approximation by Fourier series of integrable functions

Abstract

We will present an estimation of the $H_{k_0,k_r}^{q}f$  and means as a approximation versions \ of \ the Totik type generalization$(\text{see \cite{11, 12}}) $ \ of the results of \ J. Marcinkiewicz and A. Zygmund in \cite{JM, ZA}. As a measure of such approximations we will use the function constructed on the base of definition of the Gabisonia points \cite{1}. Some results on the norm approximation will also given.