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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Hardy's inequality ： ウィキペディア英語版 Hardy's inequality Hardy's inequality is an inequality in mathematics, named after G. H. Hardy. It states that if $a\_1,\; a\_2,\; a\_3,\; \backslash dots$ is a sequence of non-negative real numbers which is not identically zero, then for every real number ''p'' > 1 one has : An integral version of Hardy's inequality states if ''f'' is an integrable function with non-negative values, then :$\backslash int\_0^\backslash infty\; \backslash left\; (\backslash frac\backslash int\_0^x\; f(t)\backslash ,\; dt\backslash right)^p\backslash ,\; dx\backslash le\backslash left\; (\backslash frac\backslash right\; )^p\backslash int\_0^\backslash infty\; f(x)^p\backslash ,\; dx.$ Equality holds if and only if ''f''(''x'') = 0 almost everywhere. Hardy's inequality was first published and proved (at least the discrete version with a worse constant) in 1920 in a note by Hardy. The original formulation was in an integral form slightly different from the above. ==See also== * Carleman's inequality 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hardy's inequality」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.