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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 Stein–Strömberg theorem ： ウィキペディア英語版 Stein–Strömberg theorem In mathematics, the Stein–Strömberg theorem or Stein–Strömberg inequality is a result in measure theory concerning the Hardy–Littlewood maximal operator. The result is foundational in the study of the problem of differentiation of integrals. The result is named after the mathematicians Elias M. Stein and Jan-Olov Strömberg. ==Statement of the theorem== Let ''λ''''n'' denote ''n''-dimensional Lebesgue measure on ''n''-dimensional Euclidean space R''n'' and let ''M'' denote the Hardy–Littlewood maximal operator: for a function ''f'' : R''n'' → R, ''Mf'' : R''n'' → R is defined by :$Mf(x)\; =\; \backslash sup\_\; \backslash frac1\; (x)\; \backslash big)\}\; \backslash int\_\; |\; f(y)\; |\; \backslash ,\; \backslash mathrm\; \backslash lambda^\; (y),$ where ''B''''r''(''x'') denotes the open ball of radius ''r'' with center ''x''. Then, for each ''p'' > 1, there is a constant ''C''''p'' > 0 such that, for all natural numbers ''n'' and functions ''f'' ∈ ''L''''p''(R''n''; R), :$\backslash |\; Mf\; \backslash |\_\; \backslash |\; f\; \backslash |\_\}\; \backslash leq\; C\_\; \backslash |\; f\; \backslash |\_\{L^\{p\}\}$ for all ''f'' ∈ ''L''''p''(R''n''; R). Thus, the Stein–Strömberg theorem is the statement that the Hardy–Littlewood maximal operator is of strong type (''p'', ''p'') uniformly with respect to the dimension ''n''. 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「Stein–Strömberg theorem」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.