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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 Riesz rearrangement inequality ： ウィキペディア英語版 Riesz rearrangement inequality In mathematics, the Riesz rearrangement inequality (sometimes called Riesz-Sobolev inequality)states that for any three non-negative functions ''f,g,h'', the integral :$I(f,g,h)\; =\; \backslash iint\_^n\}\; f(x)\; g(x-y)\; h(y)\; \backslash ,\; dxdy$ satisfies the inequality :$I(f,g,h)\; \backslash leq\; I(f^$ *,g^ *,h^ *) where $f^$ *,g^ *,h^ * are the symmetric decreasing rearrangements of the functions ''f,g,'' and ''h,'' respectively. The inequality was first proved by Frigyes Riesz in 1930, and independently reproved by S.L.Sobolev in 1938. It can be generalized to arbitrarily (but finitely) many functions acting on arbitrarily many variables. In the case where any one of the three functions is a strictly symmetric-decreasing function, equality holds only when the other two functions are equal, up to translation, to their symmetric-decreasing rearrangements. ==Sources== * 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「Riesz rearrangement 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.