A sharp boundedness result for restricted maximal operators of Vilenkin-Fourier series on martingale Hardy spaces

2018/02/14 by I. Blahota, István Blahota, Károly Nagy +9
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Mathematical Analysis and Transform Methods #math.CA #msc:42B25 #msc:42C10

paper · pdf · doi:10.48550/arxiv.1802.07761

arxiv created 2018/02/14 · arxiv updated 2018/02/23

Abstract

The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space %H_p to the Lebesgue space L_p for all 0<p≤ 1. We also prove that the result is sharp in a particular sense.

Related

• Ph.D. Thesis-Martingale Hardy spaces and summability of the one dimensional Vilenkin-Fourier series
• On the convergence of partial sums with respect to Vilenkin system on the martingale Hardy spaces
• On some weighted maximal operators of partial sums of Walsh-Fourier series in the space H₁
• A sharp boundedness result concerning some maximal operators of Vilenkin-Fejér means
• Some new restricted maximal operators of Fejér means of Walsh-Fourier series in the space H_1/2