The main aim of this paper is to find necessary and sufficient conditions for the convergence of Walsh–Marcinkiewicz means in terms of the modulus of continuity on the Hardy space .
"Approximation by Walsh–Marcinkiewicz means on the Hardy space ." Kyoto J. Math. 54 (3) 641 - 652, Fall 2014. https://doi.org/10.1215/21562261-2693469