Maximal operators of Vilenkin-Nörlund means

Abstract

In this paper we prove and discuss some new $\left(H_p,weak-L_p\right)$ type inequalities of maximal operators of Vilenkin-Nörlund means with monotone coefficients. We also apply these results to prove a.e. convergence of such Vilenkin-Nörlund means. 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.

References in corpus (2)

• Fejér means of Vilenkin-Fourier series
• The maximal operators of logarithmic means of one-dimensional Vilenkin-Fourier series