Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 17, No. 2, pp. 121-126 (2001)

On the Fejér kernel functions with respect to the Walsh-Kaczmarz system

György Gát

College of Nyíregyháza, Institute of Mathematics and Computer Science, Nyíregyháza, P.O. Box 166., H-4401, Hungary gatgy@zeus.nyf.hu

Abstract: Let $G$ be the Walsh group. In this paper we prove that the integral of the maximal function of the Walsh-Kaczmarz-Fejér kernels is infinite on every interval. This is a sharp contrast with the Walsh-Paley system.

Keywords: Walsh-Paley and Walsh-Kaczmarz system.

Classification (MSC2000): 42C10

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