Lebesgue points and convergence over cone-like sets

Research output: Contribution to journalArticle


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
Issue number1
Publication statusPublished - Jan 1 2017



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

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis

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