Abstract
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 Hp into Lp for every 1/2<p⩽1. From this it follows by standard arguments that σ* is of weak type (1, 1) and bounded from Lq into Lq if 1<q⩽∞.
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