圆弧上的Lp Markov-Bernstein不等式

J. Approx. Theory Pub Date : 1900-01-01 DOI:10.1006/jath.2000.3502

D. Lubinsky

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引用次数: 12

摘要

设0 p α β≥2 π。我们证明了对于阶次为n的三角多项式s n，我们有[公式]，其中c与α， β， n, sn无关。其基本特征是估计的α和β的均匀性。这个结果可以看作是维登斯基不等式的一个L - p形式。

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Lp Markov-Bernstein Inequalities on Arcs of the Circle

Abstract Let 0 p α β ⩽2 π . We prove that for trigonometric polynomials s n of degree ⩽ n , we have[formula]where c is independent of α , β , n , s n . The essential feature is the uniformity in α and β of the estimate. The result may be viewed as an L p form of Videnskii's inequalities.

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J. Approx. Theory

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