Uniform and L-convergence of logarithmic means of Walsh-Fourier series

G. Gát, U. Goginava

Research output: Contribution to journalArticlepeer-review

40 Citations (Scopus)

Abstract

The (Nörlund) logarithmic means of the Fourier series of the integrable function f is: 1/ln Σk=1n-1 Sk (f)/n -k, where ln:= Σk=1n-1 1/k. In this paper we discuss some convergence and divergence properties of this logarithmic means of the Walsh-Fourier series of functions in the uniform, and in the L1 Lebesgue norm. Among others, as an application of our divergence results we give a negative answer to a question of Moricz concerning the convergence of logarithmic means in norm.

Original languageEnglish
Pages (from-to)497-506
Number of pages10
JournalActa Mathematica Sinica, English Series
Volume22
Issue number2
DOIs
Publication statusPublished - Apr 2006
Externally publishedYes

Keywords

  • Convergence divergence properties
  • Nörlund logarithmic means
  • Walsh system

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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