A weak-type inequality for uniformly bounded trigonometric polynomials

被引：0
|
作者：
E. D. Livshits
机构：
[1] Evernote Corporation,
来源：
Proceedings of the Steklov Institute of Mathematics | 2013年 / 280卷
关键词：
STEKLOV Institute; Trigonometric Polynomial; Interpolation Formula; Disjoint Interval; Auxiliary Lemma;
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摘要：
This paper is devoted to refining the Bernstein inequality. Let D be the differentiation operator. The action of the operator Λ = D/n on the set of trigonometric polynomials Tn is studied: the best constant is sought in the inequality between the measures of the sets {x ∈ T: |Λt(x)| > 1} and {x ∈ T: |t(x)| > 1}. We obtain an upper estimate that is order sharp on the set of uniformly bounded trigonometric polynomials TnC = {t ∈ Tn: ‖t‖ ≤ C}.
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页码：208 / 219
页数：11
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