Estimates from below for Lebesgue Constants

E. R. Liflyand, A. G. Ramm, A. I. Zaslavsky

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11 Scopus citations


Estimates from below for the norms of linear means of multiple Fourier series are obtained. These means are given by some function λ. and generalize the well-known Bochner- Riesz means. Sharpness of these estimates is established. The assumptions on λ are rather weak and of local character. Our results contain as particular cases a number of earlier published results. Proofs are based on the authors' new results on asymptotics of the Fourier transform of piecewise-smooth functions. Some applications of the results obtained are given, namely, orders of growth of the Lebesgue constants for "ovals" and "hyperbolic crosses" are evaluated and sharp conditions on the modulus of smoothness of a function are given, for this function to be approximated by the linear means.

Original languageEnglish
Pages (from-to)287-301
Number of pages15
JournalJournal of Fourier Analysis and Applications
Issue number3
StatePublished - Jun 1995


  • Lebesgue constants
  • Legendre transform
  • Radon transform


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