English

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

Classical Analysis and ODEs 2016-08-14 v2

Abstract

We will present an estimation of the Hk0,krqfH_{k_{0},k_{r}}^{q}f  \ and % H_{u}^{\lambda \varphi}f means as a approximation versions \ of \ the Totik type generalization(see \cite11, 12)(\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.

Keywords

Cite

@article{arxiv.1204.1281,
  title  = {Pointwise strong and very strong approximation by Fourier series of integrable functions},
  author = {Włodzimierz Łenski},
  journal= {arXiv preprint arXiv:1204.1281},
  year   = {2016}
}