Some inequalities related to strong convergence of Riesz logarithmic means

[摘要] 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.

[学科分类] 电力

[关键词] Inequalities;Vilenkin systems;Walsh system;Riesz logarithmic means;Martingale Hardy space;Strong convergence