On the maximal operators of Fejér means with respect to the character system of the group of 2-adic integers in hardy spaces

It was a question of Taibleson, open for a long time that the almost everywhere convergence of Fejér (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 Gá t in 1997. The aim of this paper is to investigate the maximal operator of the supn |σn|. Among other things, we prove that this operator is bounded from the Hardy space Hp to the Lebesgue space Lp if and only if 1/2 < p < ∞. The two-dimensional maximal operator is also discussed.