Some new restricted maximal operators of Fejér means of Walsh-Fourier series in the space H_1/2

2023/02/18 by Davit Baramidze, Baramidze, Davit, Lars‐Erik Persson +3
Mathematics · #42C10 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2302.12997

openalex publication_date 2023/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we derive the maximal subspace of natural numbers \n_k:k≥ 0\, such that the restricted maximal operator, defined by sup_{k∈ ℕ}\vert σ_n_kF \vert on this subspace of Fejér means of Walsh-Fourier series is bounded from the martingale Hardy space H_1/2 to the Lebesgue space L_1/2. The sharpness of this result is also proved.

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