Date: 17 Apr 2013
Some Inequalities for Derivatives of Trigonometric and Algebraic Polynomials
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
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  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.
h. Kilgore, On Weighted Simultaneous Approximation, Acta Math. Hung., submitted.
M. Feiten, A modulus of smoothness based on an algebraic addition, Aequationes Mathematicae, to appear.
M. Feiten, Characterization of best algebraic approximation by an algebraic modulus of smoothness, J. Approx. Theory, to appear.
B. Opic and A. Kufner, “Hardy-type inequalities,” Longman Scientific & Technical, 1990.
- Some Inequalities for Derivatives of Trigonometric and Algebraic Polynomials
Results in Mathematics
Volume 30, Issue 1-2 , pp 79-92
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- Polynomial inequalities
- Brudnyi’s inequality
- weighted spaces
- Muckenhoupt A p condition
- moduli of smoothness