Some new (H_p,L_p) type inequalities of maximal operators of Vilenkin-Nörlund means with non-decreasing coefficients

2015/04/21 by L. E. Persson, Persson, L. E., G. Tephnadze +3
Mathematics · #42B25 #42C10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:42B25 #msc:42C10

paper · pdf · doi:10.48550/arxiv.1504.05974

arXiv admin note: text overlap with arXiv:1503.05396, arXiv:1410.7978, arXiv:1504.05779

arxiv created 2015/04/21 · arxiv updated 2015/04/24

Abstract

In this paper we prove and discuss some new (H_p,L_p) type inequalities of maximal operators of Vilenkin-Nörlund means with non-decreasing coefficients. We also apply these inequalities to prove strong convergence theorems of such Vilenkin-Nörlund means. These inequalities are the best possible in a special sense. As applications, both some well-known and new results are pointed out.

Citations

• Maximal operators of Vilenkin-Nörlund means
• A sharp boundedness result concerning some maximal operators of Vilenkin-Fejér means
• On the Nörlund means of Vilenkin-Fourier series

Related

• On the Nörlund means of Vilenkin-Fourier series
• Sharp ( H_p,L_p) type inequalities of maximal operators of T means with respect to Vilenkin systems with monotone coefficients
• A note on The maximal operators of the Nörlund logaritmic means of Vilenkin-Fourier series
• Maximal operators of T means with respect to the Vilenkin system
• On the maximal operators of Walsh-Kaczmarz-Nörlund means