Results in Mathematics

, Volume 30, Issue 1, pp 79-92

First online:

Some Inequalities for Derivatives of Trigonometric and Algebraic Polynomials

  • Theodore KilgoreAffiliated withMathematics, Auburn University Email author 
  • , Michael FeltenAffiliated withMathematik VIII, Universität Dortmund

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We investigate inequalities for derivatives of trigonometric and algebraic polynomials in weighted L P spaces with weights satisfying the Muckenhoupt A p 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 A p condition moduli of smoothness