On the Cesaro summability with respect to the Walsh-Kaczmarz system

[摘要] The Walsh system will be considered in the Kaczmarz rearrangement. We show that the maximal operator sigma* 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 < p 1. From this it follows by standard arguments that sigma* is of weak type (1, 1) and bounded from L(q) into L(q) if 1 < q infinity. (C) 2000 Academic Press.

[发布日期] 2000-10-01