Kilgore, T. & Felten, M. Results. Math. (1996) 30: 79. doi:10.1007/BF03322182
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  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.
Key words and phrases
Polynomial inequalitiesBrudnyi’s inequalityweighted spacesMuckenhoupt Ap conditionmoduli of smoothness