, Volume 30, Issue 1-2, pp 79-92

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 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.