Walsh-Lebesgue points and restricted convergence of multi-dimensional Walsh-Fourier series

Research output: Contribution to journalArticle

Abstract

A new concept of Walsh-Lebesgue points is introduced for higher dimensions and it is proved that almost every point is a modified Walsh-Lebesgue point of an integrable function. It is shown that the Walsh-Fejér means σnf of a function f ∈ L1[0, 1)d converge to f at each modified Walsh-Lebesgue point, whenever n→∞ and n is in a cone. The same is proved for other summability means, such as for the Weierstrass, Abel, Picard, Bessel, Cesàro, de La Vallée-Poussin, Rogosinski and Riesz summations. xs

Original languageEnglish
Pages (from-to)97-118
Number of pages22
JournalStudia Scientiarum Mathematicarum Hungarica
Volume54
Issue number1
DOIs
Publication statusPublished - Mar 1 2017

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Lebesgue Point
Fourier series
Friedrich Wilhelm Bessel
Summability
Summation
Higher Dimensions
Cone
Converge

Keywords

  • Interpolation
  • Martingale hardy spaces
  • P-atoms
  • Summability
  • Walsh functions
  • Walsh-Lebesgue point

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Walsh-Lebesgue points and restricted convergence of multi-dimensional Walsh-Fourier series. / Weisz, F.

In: Studia Scientiarum Mathematicarum Hungarica, Vol. 54, No. 1, 01.03.2017, p. 97-118.

Research output: Contribution to journalArticle

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