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

2020/07/28 by George Tephnadze, Tephnadze, George
Mathematics · #42C10 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2008.00941

openalex publication_date 2020/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove and discuss some new ( H_p,L_p) 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.

Citations

• A note on The maximal operators of the Nörlund logaritmic means of Vilenkin-Fourier series
• Convergence and Strong Summability of the Two-dimensional\n Vilenkin-Fourier Series

Related

• On the Partial Sums and Marcinkiewicz and Fejér Means on the One- and Two-dimensional One-parameter Martingale Hardy Spaces
• On the boundedness of subsequences of Vilenkin-Fejér means on the martingale Hardy spaces
• Strong convergence theorem for Walsh-Kaczmarz-Fejér means
• Ph.D. Thesis-Martingale Hardy spaces and summability of the one dimensional Vilenkin-Fourier series
• On the partial sums of Walsh-Fourier series