ℓ1-summability and Lebesgue points of d-dimensional fourier transforms

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Abstract

The classical Lebesgue's theorem is generalized, and it is proved that under some conditions on the summability function θ, the ℓ1-θ-means of a function f from the Wiener amalgam space W(L1; ℓ)(ℝd) ⊃ L1(ℝd) converge to f at each modified strong Lebesgue point and thus almost everywhere. The θ-summability contains the Weierstrass, Abel, Picard, Bessel, Fejér, de La Vallée-Poussin, Rogosinski, and Riesz summations.

Original languageEnglish
Pages (from-to)284-304
Number of pages21
JournalAdvances in Operator Theory
Volume4
Issue number1
DOIs
Publication statusPublished - Jan 1 2019

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Keywords

  • Fejér summability
  • Fourier transforms
  • L1-summability
  • Lebesgue points
  • θ- summability

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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