, Volume 30, Issue 1-2, pp 79-92
Date: 17 Apr 2013

Some Inequalities for Derivatives of Trigonometric and Algebraic Polynomials

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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.