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Some remarks on Turán's inequality. III: The completion

Некоторые замечания о неравенствах Туран а. III: Заключение

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Abstract

Устанавливается сле дующее неравенство т ипа неравенства Турана. П усть 0<p<q<∞, 1−1/p+1/p≥0. Еслиf(x) — де йствительный алгебраический многочлен степени не вышеn, все нули которо го лежат на [−1,1], то

$$\left( {\int_{ - 1}^1 {\left| {f'(x)} \right|^p dx} } \right)^{1/p} \geqslant C^* \sqrt n ^{1 - 1/p + 1/q} \left( {\int_{ - 1}^1 {\left| {f(x)} \right|^q dx} } \right)^{1/q} .$$

Эта работа завершает цикл исследований ав тора, относящихся к этой за даче.

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Author notes

  1. S. P. Zhou

    Present address: Department of Mathematics, Hangzhou University, Hangzhou, 310 028, Zhejiang, People's Republic of China

Authors and Affiliations

  1. Department of Mathematics, University of Alberta, T6G 2G1, Edmonton, Alberta, Canada

    S. P. Zhou

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Supported in part by NSERC Canada.

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Zhou, S.P. Some remarks on Turán's inequality. III: The completion. Analysis Mathematica 21, 313–318 (1995). https://doi.org/10.1007/BF01909153

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  • DOI: https://doi.org/10.1007/BF01909153

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