Some Inequalities for Trigonometric Polynomials and their Derivatives

Knoop, Hans-Bernd; Zhou, Xiaoying

doi:10.1007/978-3-0348-8696-3_6

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2007

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Cited by 3 publications

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“…We need also the following inequality (see [4]): for k ≥ 1 there is a constant C > 0 such that for all > 0, all n = 1, 2, ..., and all t n ∈ Π n t (k)…”

Section: Proof Of Theoremsmentioning

confidence: 99%

Lower bounds of some singular integrals and their applications

Xie

Zhou

2007

Arch. Math.

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“…We need also the following inequality (see [4]): for k ≥ 1 there is a constant C > 0 such that for all > 0, all n = 1, 2, ..., and all t n ∈ Π n t (k)…”

Section: Proof Of Theoremsmentioning

confidence: 99%

Lower bounds of some singular integrals and their applications

Xie

Zhou

2007

Arch. Math.

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Inequalities for Trigonometric Polynomials and Some Integral Means

Knoop¹,

Zhou²

2001

Journal of Mathematical Analysis and Applications

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Some inequalities associated with the Laplacian for trigonometric polynomials are given, which will be applied to investigate the behavior in approximation by trigonometric polynomials in higher dimensions and the best lower and upper estimates for some linear operators. In particular, we obtain a complete characterization for the approximation behavior of the classical Jackson operator. Thus the approximation error of a function by Jackson polynomials is equivalent to a K-functional defined by the Laplacian.

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