Approximation by Θ-Means of Walsh—Fourier Series in Dyadic Hardy Spaces and Dyadic Homogeneous Banach Spaces

I. Blahota, K. Nagy, M. Salim

Research output: Contribution to journalArticlepeer-review

Abstract

In this article we discuss the behaviour of Θ-means of Walsh—Fourier series of a function in dyadic Hardy spaces Hp and dyadic homogeneous Banach spaces X. Namely, we estimate the rate of the approximation by Θ-means in terms of modulus of continuity in X and best approximation in Hp. Our main theorem is a generalization of a result of Fridli, Manchanda and Siddiqi [7]. Moreover, it extends a previous result of the authors [3]

Original languageEnglish
Pages (from-to)285-309
Number of pages25
JournalAnalysis Mathematica
Volume47
Issue number2
DOIs
Publication statusPublished - Jun 2021

Keywords

  • Fejér mean
  • Nörlund mean
  • Walsh group
  • Walsh system
  • Walsh—Fourier series
  • approximation
  • dyadic Hardy space
  • dyadic homogeneous Banach space
  • modulus of continuity
  • weighted mean
  • Θ-mean

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)

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