On the Fejér means of bounded Ciesielski systems

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Abstract

We investigate the bounded Ciesielski systems, which can be obtained from the spline systems of order (m, k) in the same way as the Walsh system arises from the Haar system. It is shown that the maximal operator of the Fejér means of the Ciesielski-Fourier series is bounded from the Hardy space Hp to Lp if 1/2 < p < ∞ and m ≥ 0, |k| ≤ m + 1. Moreover, it is of weak type (1, 1). As a consequence, the Fejér means of the Ciesielski-Fourier series of a function f converges to f a.e. if f ∈ L1 as n → ∞.

Original languageEnglish
Pages (from-to)227-243
Number of pages17
JournalStudia Mathematica
Volume146
Issue number3
DOIs
Publication statusPublished - Jan 1 2001

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Keywords

  • Atomic decomposition
  • Fejér means
  • Hardy spaces
  • Interpolation
  • Spline systems
  • p-atom

ASJC Scopus subject areas

  • Mathematics(all)

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