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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 Littlewood subordination theorem ： ウィキペディア英語版 Littlewood subordination theorem In mathematics, the Littlewood subordination theorem, proved by J. E. Littlewood in 1925, is a theorem in operator theory and complex analysis. It states that any holomorphic univalent self-mapping of the unit disk in the complex numbers that fixes 0 induces a contractive composition operator on various function spaces of holomorphic functions on the disk. These spaces include the Hardy spaces, the Bergman spaces and Dirichlet space. ==Subordination theorem== Let ''h'' be a holomorphic univalent mapping of the unit disk ''D'' into itself such that ''h''(0) = 0. Then the composition operator ''C''''h'' defined on holomorphic functions ''f'' on ''D'' by :$C\_h(f)\; =\; f\backslash circ\; h$ defines a linear operator with operator norm less than 1 on the Hardy spaces $H^p(D)$, the Bergman spaces $A^p(D)$. (1 ≤ ''p'' < ∞) and the Dirichlet space $\backslash mathcal(D)$. The norms on these spaces are defined by: :$\backslash |f\backslash |\_^p\; =\; \backslash sup\_r\; \backslash int\_0^\; |f(re^)|^p\; \backslash ,\; d\backslash theta$ :$\backslash |f\backslash |\_^p\; =\; \backslash iint\_D\; |f(z)|^p\backslash ,\; dx\backslash ,dy$ :$\backslash |f\backslash |\_^2\; =\; \backslash iint\_D\; |f^\backslash prime(z)|^2\backslash ,\; dx\backslash ,dy=\; \backslash iint\_D\; |\backslash partial\_x\; f|^2\; +\; |\backslash partial\_y\; f|^2\backslash ,\; dx\backslash ,dy$ 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「Littlewood subordination 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.