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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 Muckenhoupt weights ： ウィキペディア英語版 Muckenhoupt weights In mathematics, the class of Muckenhoupt weights consists of those weights for which the Hardy–Littlewood maximal operator is bounded on . Specifically, we consider functions on and their associated maximal functions defined as :$M(f)(x)\; =\; \backslash sup\_\; \backslash frac\; \backslash int\_\; |f|,$ where is the ball in with radius and centre . Let , we wish to characterise the functions for which we have a bound :$\backslash int\; |M(f)(x)|^p\; \backslash ,\; \backslash omega(x)\; dx\; \backslash leq\; C\; \backslash int\; |f|^p\; \backslash ,\; \backslash omega(x)\backslash ,\; dx,$ where depends only on and . This was first done by Benjamin Muckenhoupt. ==Definition== For a fixed , we say that a weight belongs to if is locally integrable and there is a constant such that, for all balls in , we have : where is the Lebesgue measure of , and is a real number such that: . We say belongs to if there exists some such that : $\backslash frac\; \backslash int\_B\; \backslash omega(x)\; \backslash ,\; dx\; \backslash leq\; C\backslash omega(x),$ for all and all balls . 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「Muckenhoupt weights」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.