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

Gy Gát, U. Goginava

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21 Citations (Scopus)

Abstract

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).

Original languageEnglish
Pages (from-to)65-83
Number of pages19
JournalActa Mathematica Hungarica
Volume125
Issue number1
DOIs
Publication statusPublished - 2009
Externally publishedYes

Keywords

  • Cesàro means
  • Hardy space
  • Walsh-Kaczmarz system

ASJC Scopus subject areas

  • General Mathematics

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