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Walsh-Marcinkiewicz means and Hardy spaces |
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| Authors: | Károly Nagy George Tephnadze |
| Affiliation: | 1. Institute of Mathematics and Computer Sciences, College of Nyíregyháza, P.O. Box 166, Nyíregyháza, 4400, Hungary 2. Department of Mathematics, Faculty of Exact and Natural Sciences, Tbilisi State University, Chavchavadze St. 1, Tbilisi, 0128, Georgia 3. Department of Engineering Sciences and Mathematics, Lule? University of Technology, 971 87, Lule?, Sweden |
| Abstract: | The main aim of this paper is to investigate the Walsh-Marcinkiewicz means on the Hardy space H p , when 0 < p < 2/3. We define a weighted maximal operator of Walsh-Marcinkiewicz means and establish some of its properties. With its aid we provide a necessary and sufficient condition for convergence of the Walsh-Marcinkiewicz means in terms of modulus of continuity on the Hardy space H p , and prove a strong convergence theorem for the Walsh-Marcinkiewicz means. |
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