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Some Identities and Inequalities for Derivatives

✍ Scribed by K. Balazs; T. Kilgore

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
336 KB
Volume
82
Category
Article
ISSN
0021-9045

No coin nor oath required. For personal study only.

✦ Synopsis

We introduce some identities for the derivative of a trigonometric polynomial which are obtained from the identity of Riesz. We then use these new identities to derive some inequalities for derivatives of trigonometric and algebraic polynomials. Among our results are a weighted (L^{p}) inequality relating the derivative of a trigonometric polynomial to its (L^{p}) modulus and simple proofs for the inequalities of Brudnyi and Dzyadyk. We are able to give values to the constants in these inequalitics. if 1995 Academic Press. Inc.

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