The One-dimensional Martingale Hardy Spaces and Partial Sums and Fejér Means with respect to Walsh system

Abstract

In this paper we prove and discuss some new $\left(H_p,L_p\right)$ type inequalities for partial Sums and Fejér means with respect to Walsh system. 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 (6)

• Fejér means of Vilenkin-Fourier series
• A note on the norm convergence by Vilenkin-Fejér means
• A note on the Fourier coefficients and partial sums of Vilenkin-Fourier series
• The maximal operators of logarithmic means of one-dimensional Vilenkin-Fourier series
• A note on the strong convergence of two-dimensional Walsh-Fourier series
• A note on The maximal operators of the Nörlund logaritmic means of Vilenkin-Fourier series