Weighted maximal operators of Fejér means of Walsh-Fourier series in the martingale Hardy space H_1/2

2023/02/18 by N. Areshidze, Areshidze, Nika, Davit Baramidze +5
Mathematics · #Advanced Harmonic Analysis Research #Differential Equations and Boundary Problems #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2302.12302

Abstract

In this paper we derive the restricted weighted maximal operator, defined by sup _{k∈ ℕ}(\vert σ_kF\vert/A²_k) of Fejér means of Walsh-Fourier series and prove that the it is bounded from the martingale Hardy space H_1/2(G) to the Lebesgue space L_1/2(G). The sharpness of this result is also proved. As a consequence we obtain some new and and well-know results.

Related

• Some new restricted maximal operators of Fejér means of Walsh-Fourier series in the space H_1/2
• On some weighted maximal operators of partial sums of Walsh-Fourier series in the space H₁
• Some new weak (H_p-L_p) type inequality for weighted maximal operators of Walsh-Fourier series
• Strong convergence theorem for Walsh-Kaczmarz-Fejér means
• Variable Martingale Hardy Spaces and Their Applications in Fourier Analysis