Ukrainian Mathematical Journal

, Volume 66, Issue 11, pp 1731–1741 | Cite as

Best Approximations for the Cauchy Kernel on the Real Axis

  • V. M. Savchuk
  • S. O. Chaichenko

We compute the values of the best approximations for the Cauchy kernel on the real axis ℝ by some subspaces from L q (ℝ). This result is applied to the evaluation of the sharp upper bounds for pointwise deviations of certain interpolation operators with interpolation nodes in the upper half plane and certain linear means of the Fourier series in the Takenaka–Malmquist system from the functions lying in the unit ball of the Hardy space H p , 2 ≤ p < ∞.


Fourier Series Unit Ball Unit Disk Real Axis Hardy Space 
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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • V. M. Savchuk
    • 1
  • S. O. Chaichenko
    • 2
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine
  2. 2.Donbass State Pedagogic UniversitySlavyanskUkraine

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