文摘
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 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. Keywords group of 2-adic integers character system Fejér mean Fourier series Hardy space maximal operator