On the Cesaro Summability with Respect to the Walsh–Kaczmarz System

The Walsh system will be considered in the Kaczmarz rearrangement. We show that the maximal operator σ* of the (C,1)-means of the Walsh–Kaczmarz–Fourier series is bounded from the dyadic Hardy space H^p into L^p for every 1/2<p1. From this it follows by standard arguments that σ* is of weak type (1, 1) and bounded from L^q into L^q if 1<q∞.