English

On the maximal operators of $T$ means with respect to Walsh-Kaczmarz system

Classical Analysis and ODEs 2021-03-30 v2 Analysis of PDEs

Abstract

In this paper we prove and discuss some new (Hp,Lp,)\left( H_p,L_{p,\infty}\right) type inequalities of the maximal operators of TT means with monotone coefficients with respect to Walsh-Kaczmarz system. It is also proved that these results are the best possible in a special sense. As applications, both some well-known and new results are pointed out. In particular, we apply these results to prove a.e. convergence of such TT means.

Keywords

Cite

@article{arxiv.2007.14455,
  title  = {On the maximal operators of $T$ means with respect to Walsh-Kaczmarz system},
  author = {Nata Gogolashvili and George Tephnadze},
  journal= {arXiv preprint arXiv:2007.14455},
  year   = {2021}
}