Results in Mathematics

, Volume 30, Issue 1, pp 79–92

Some Inequalities for Derivatives of Trigonometric and Algebraic Polynomials

Article

DOI: 10.1007/BF03322182

Cite this article as:
Kilgore, T. & Felten, M. Results. Math. (1996) 30: 79. doi:10.1007/BF03322182
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Abstract

We investigate inequalities for derivatives of trigonometric and algebraic polynomials in weighted LP spaces with weights satisfying the Muckenhoupt Ap condition. The proofs are based on an identity of Balázs and Kilgore [1] for derivatives of trigonometric polynomials. Also an inequality of Brudnyi in terms of rth order moduli of continuity ωr will be given. We are able to give values to the constants in the inequalities.

AMS Classification

26D0541A1742A05

Key words and phrases

Polynomial inequalitiesBrudnyi’s inequalityweighted spacesMuckenhoupt Ap conditionmoduli of smoothness

Copyright information

© Birkhäuser Verlag, Basel 1996

Authors and Affiliations

  1. 1.MathematicsAuburn UniversityAuburnUSA
  2. 2.Mathematik VIIIUniversität DortmundDortmundGermany