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.
