A weak-type inequality for uniformly bounded trigonometric polynomials (Q2446182)
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| English | A weak-type inequality for uniformly bounded trigonometric polynomials |
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A weak-type inequality for uniformly bounded trigonometric polynomials (English)
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16 April 2014
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Considering two important examples of operators, \textit{A. G. Babenko} [Tr. Inst. Mat. Mekh. (Ekaterinburg) 2, 34--41 (1992; Zbl 0813.42001)] obtained weak-type inequalities for trigonometric polynomials. \textit{V. V. Arestov} and \textit{A. S. Mendelev} [J. Approx. Theory 162, No. 10, 1852--1878 (2010; Zbl 1207.42001)] showed that the lower estimate in one of these inequalities is sharp. For the other inequality the author proves here that for uniformly bounded trigonometric polynomials the lower estimate is order sharp.
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trigonometric polynomials
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Bernstein's inequalities
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weak-type inequalities
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