TY - JOUR
T1 - A weak type inequality for the maximal operator of (C, α)-means of Fourier series with respect to the Walsh-Kaczmarz system
AU - Gát, Gy
AU - Goginava, U.
PY - 2009
Y1 - 2009
N2 - 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 Hp to the space Lp 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*α,k is bounded from the martingale Hardy space H1/(1+α) to the space weak-L1/(1+α).
AB - 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 Hp to the space Lp 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*α,k is bounded from the martingale Hardy space H1/(1+α) to the space weak-L1/(1+α).
KW - Cesàro means
KW - Hardy space
KW - Walsh-Kaczmarz system
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U2 - 10.1007/s10474-009-8217-8
DO - 10.1007/s10474-009-8217-8
M3 - Article
AN - SCOPUS:70450250360
SN - 0236-5294
VL - 125
SP - 65
EP - 83
JO - Acta Mathematica Hungarica
JF - Acta Mathematica Hungarica
IS - 1
ER -