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http://dx.doi.org/10.14403/jcms.2018.31.1.231

ON HARDY AND PÓLYA-KNOPP'S INEQUALITIES

Kwon, Ern Gun (Department of Mathematics Education Andong National University)
Jo, Min Ju (Department of Mathematics Graduate School, Andong National University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.31, no.2, 2018 , pp. 231-237 More about this Journal

Abstract

Hardy's inequality is refined non-trivially as the form ${\int_{0}^{{\infty}}}\{{\frac{1}{x}}{\int_{0}^{x}}f(t)dt\}^pdx{\leq}Q_f{\times}({\frac{p}{p-1}})^p{\int_{0}^{x}}f^p(x)dx$ for some $Q_f:0{\leq}Q_f{\leq}1$ . $P{\acute{o}}lya$ -Knopp's inequality is also refined by the similar form.

Keywords

Minkowski's inequality; Hardy's inequality; $P{\acute{o}}lya$ -Knopp's inequality;

Citations & Related Records

Reference

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