Results in Mathematics

, Volume 30, Issue 1–2, pp 79–92 | Cite as

Some Inequalities for Derivatives of Trigonometric and Algebraic Polynomials

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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

26D05 41A17 42A05 

Key words and phrases

Polynomial inequalities Brudnyi’s inequality weighted spaces Muckenhoupt Ap condition moduli of smoothness 

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References

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    K. Balázs and Th. Kilgore, Some Identities and Inequalities for Derivatives, J. Approx. Theory 82 (1995), 274–286.MathSciNetMATHCrossRefGoogle Scholar
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    h. Kilgore, On Weighted Simultaneous Approximation, Acta Math. Hung., submitted.Google Scholar
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    M. Feiten, Characterization of best algebraic approximation by an algebraic modulus of smoothness, J. Approx. Theory, to appear.Google Scholar
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    B. Muckenhoupt, Hardy’s inequality with weights, Studia Math. 44 (1972), 31–38.MathSciNetMATHGoogle Scholar
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    B. Opic and A. Kufner, “Hardy-type inequalities,” Longman Scientific & Technical, 1990.Google Scholar

Copyright information

© Birkhäuser Verlag, Basel 1996

Authors and Affiliations

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

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