Sharp H p $H_{p}$ - L p $L_{p}$ type inequalities of weighted maximal operators of Vilenkin-Nörlund means and its applications

Abstract

Abstract We prove and discuss some new H p $H_{p}$ - L p $L_{p}$ type inequalities of weighted maximal operators of Vilenkin-Nörlund means with monotone coefficients. It is also proved that these inequalities are the best possible in a special sense. We also apply these results to prove strong summability for such Vilenkin-Nörlund means. As applications, both some well-known and new results are pointed out.

Keywords

• inequalities
• Vilenkin system
• Vilenkin group
• Nörlund means
• martingale Hardy space
• L p $L_{p}$ spaces