Maximal operators of $T$ means with respect to the Vilenkin system

Abstract

In this paper we prove and discuss some new $\left(H_p,weak-L_p\right)$ type inequalities of maximal operators of $T$ means with respect to Vilenkin systems with monotone coefficients. We also apply these results to prove a.e. convergence of \ such $T$ means. It has also been proven that these results are the best possible in a special sense. As applications, both well-known and new results are highlighted.

Cited by in corpus (3)

• Sharp $\left(H_p,L_p\right)$ type inequalities of maximal operators of $T$ means with respect to Vilenkin systems with monotone coefficients
• Lebesgue and Vilenkin-Lebesgue points and a.e. Convergence of T means with respect to Vilenkin systems of integrable functions
• Sharp $(H_p,L_p)$ and $(H_p,\text{weak}-L_p)$ type inequalities of weighted maximal operators of $T$ means with respect to Vilenkin systems