Lebesgue points and convergence over cone-like sets

Research output: Contribution to journalArticle

Abstract

We generalize the well known Lebesgue's theorem about the convergence of Fejér means for higher dimensions. Under some conditions on θ, we show that the summability means σT θ f of a function f from the largest Wiener amalgam space W(L1, ℓ∞)(ℝd) converge to f at each modified Lebesgue point, whenever T → ∞ and T is in a cone-like set. The result holds for the Weierstrass, Abel, Picar, Bessel, Fejér, Cesàro, de La Vallée-Poussin, Rogosinski and Riesz summations.

Original languageEnglish
Pages (from-to)65-83
Number of pages19
JournalJaen Journal on Approximation
Volume9
Issue number1
Publication statusPublished - Jan 1 2017

Fingerprint

Lebesgue Point
Mercury amalgams
Cones
Wiener Amalgam Spaces
Cone
Friedrich Wilhelm Bessel
Summability
Henri Léon Lebésgue
Summation
Higher Dimensions
Converge
Generalise
Theorem

Keywords

  • Cone-like sets
  • Fejér summability
  • Fourier series
  • Fourier transforms
  • Lebesgue points
  • θ-summability

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis

Cite this

Lebesgue points and convergence over cone-like sets. / Weisz, Ferenc.

In: Jaen Journal on Approximation, Vol. 9, No. 1, 01.01.2017, p. 65-83.

Research output: Contribution to journalArticle

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