English

On moduli of smoothness and averaged differences of fractional order

Classical Analysis and ODEs 2017-09-12 v1

Abstract

We consider two types of fractional integral moduli of smoothness, which are widely used in theory of functions and approximation theory. In particular, we obtain new equivalences between these moduli of smoothness and the classical moduli of smoothness. It turns out that for fractional integral moduli of smoothness some pathological effects arise.

Keywords

Cite

@article{arxiv.1709.03168,
  title  = {On moduli of smoothness and averaged differences of fractional order},
  author = {Yurii Kolomoitsev},
  journal= {arXiv preprint arXiv:1709.03168},
  year   = {2017}
}