Some Inequalities for Derivatives of Trigonometric and Algebraic Polynomials
- 6 Downloads
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.
AMS Classification26D05 41A17 42A05
Key words and phrasesPolynomial inequalities Brudnyi’s inequality weighted spaces Muckenhoupt Ap condition moduli of smoothness
Unable to display preview. Download preview PDF.
- h. Kilgore, On Weighted Simultaneous Approximation, Acta Math. Hung., submitted.Google Scholar
- M. Feiten, A modulus of smoothness based on an algebraic addition, Aequationes Mathematicae, to appear.Google Scholar
- M. Feiten, Characterization of best algebraic approximation by an algebraic modulus of smoothness, J. Approx. Theory, to appear.Google Scholar
- B. Opic and A. Kufner, “Hardy-type inequalities,” Longman Scientific & Technical, 1990.Google Scholar