A weak type inequality for the maximal operator of ( C, α)-means of Fourier series with respect to the Walsh-Kaczmarz system.

Simon [12] proved that the maximal operator of ( C, α)-means of Fourier series with respect to the Walsh-Kaczmarz system is bounded from the martingale Hardy space H _p to the space L _p for p > 1/(1 + α). In this paper we prove that this boundedness result does not hold if p ≦ 1/(1 + α). However, in the endpoint case p = 1/(1 + α) the maximal operator σ is bounded from the martingale Hardy space H_{1/(1+ α)} to the space weak- L_{1/(1+ α)}. [ABSTRACT FROM AUTHOR]