歐氏空間富式分析的探討;A study of Fourier series in Euclidean spaces

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)" 1 < p≤∞" 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) "for 1 < p≤∞" . At the end, we will discuss one of the most important singular intergrals, the so-called Hilbert transform.
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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