An Estimate of the Maximal Operator of the Nörlund Logarithmic Means with Respect to the Character System of the Group of 2-adic Integers on the Hardy Space H_1

We define weighted maximal operators of each of partial sums of Fourier series ˜S ∗and Nörlund logarithmic means ˜L ∗, with respect to the character system of the group of 2-adic integers. We prove that they are bounded from H1 to L1, then establish the sharpness of these results.