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    Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/72325

    Title: 歐氏空間富式分析的探討;A study of Fourier series in Euclidean spaces
    Authors: 古文仁;Ku,Wen-Jen
    Contributors: 數學系
    Keywords: 傅利葉級數;歐氏空間;施瓦茨空间;哈代-李特爾伍德極大函數;奇異積分算子;希爾伯特轉換
    Date: 2016-06-15
    Issue Date: 2016-10-13 14:47:43 (UTC+8)
    Publisher: 國立中央大學
    Abstract: 在此篇論文裡,我們先探究在不同函數空間上的傅立葉轉換,例如說在L^1空間、在L^p空間1 < p ≤ 2及在Schwartz空間。接下來,我們會利用一些性質和定理去探究Hardy-Littlewood的極大函數,並證明其有weak (1,1)和strong(p,p)&quot; 1 < p≤∞&quot; 的性質。最後,我們將探討奇異積分算子的有界性,我們將專注在Hilbert transform。;In this thesis, we study various properties of Fourier transform. We first study the Fourier transform on Schwartz classes, and extend to L^p spaces for 1 ≤p≤2. Secondly, we shall focus on the Hardy-Littlewood maximal function, and prove that it is weak (1, 1) and strong(p, p) &quot;for 1 < p≤∞&quot; . At the end, we will discuss one of the most important singular intergrals, the so-called Hilbert transform.
    Appears in Collections:[數學研究所] 博碩士論文

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