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Ukrainian Mathematical Journal

, Volume 70, Issue 3, pp 437–466 | Cite as

On the Moduli of Smoothness with Jacobi Weights

  • K. A. Kopotun
  • D. Leviatan
  • I. A. Shevchuk
Article
  • 4 Downloads

We introduce the moduli of smoothness with Jacobi weights (1 − x)𝛼(1 + x)β for functions in the Jacobi weighted spaces Lp[1, 1], 0 < p. These moduli are used to characterize the smoothness of (the derivatives of) functions in the weighted spaces Lp . If 1 ≤ p1, then these moduli are equivalent to certain weighted K-functionals (and, hence, they are equivalent to certain weighted Ditzian–Totik moduli of smoothness for these p), while for 0 < p < 1 they are equivalent to certain “realization functionals.”

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • K. A. Kopotun
    • 1
  • D. Leviatan
    • 2
  • I. A. Shevchuk
    • 3
  1. 1.University of ManitobaWinnipegCanada
  2. 2.School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael
  3. 3.Shevchenko Kyiv National UniversityKyivUkraine

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