Some inequalities related to strong convergence of Riesz logarithmic means

Abstract

Abstract In this paper we derive a new strong convergence theorem of Riesz logarithmic means of the one-dimensional Vilenkin–Fourier (Walsh–Fourier) series. The corresponding inequality is pointed out and it is also proved that the inequality is in a sense sharp, at least for the case with Walsh–Fourier series.

Keywords

• Inequalities
• Vilenkin systems
• Walsh system
• Riesz logarithmic means
• Martingale Hardy space
• Strong convergence