On the Maximal Operators of Fejer Means with Respect to the Character System of the Group of 2-Adic Integers in Hardy Spaces

摘要

It was a question of Taibleson, open for a long time that the almost everywhere convergence of Fejer (or (C, 1)) means of Fourier series of integrable functions with respect the character system of the group of 2-adic integers. This question was answered by Gat in 1997. The aim of this paper is to investigate the maximal operator of the sup_n σ_n. Among other things, we prove that this operator is bounded from the Hardy space H_p to the Lebesgue space L_p if and only if 1/2 ＜ p ＜ ∞. The two-dimensional maximal operator is also discussed.