Ukrainian Mathematical Journal

, Volume 63, Issue 12, pp 1883–1899 | Cite as

Inequalities for trigonometric polynomials in spaces with integral metric

  • S. A. Pichugov
In the spaces L ψ (T ) of periodic functions with metric
$$ \rho {\left( {f,0} \right)_\psi } = \int\limits_T {\psi \left| {f(x)} \right|dx,} $$
where ψ is a function of the modulus-of-continuity type, we investigate analogs of the classic Bern-stein inequalities for the norms of derivatives and increments of trigonometric polynomials.


Periodic Function Trigonometric Polynomial Interpolation Formula Kernel Versus Bernstein Inequality 
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Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  • S. A. Pichugov
    • 1
  1. 1.Dnepropetrovsk National University of Railway TransportDnepropetrovskUkraine

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