Sharp $\left(H_p,L_p\right)$ type inequalities of maximal operators of $T$ means with respect to Vilenkin systems with monotone coefficients

Abstract

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

arXiv admin note: substantial text overlap with arXiv:1504.05974, arXiv:1803.00627 by other authors

References in corpus (2)

• Fejér means of Vilenkin-Fourier series
• Maximal operators of $T$ means with respect to the Vilenkin system