在這篇文章中,我們分成兩個章節。第一個章節是在介紹Hardy-Littlewood 極大函數及其應用,而它包含了Hardy-Littlewood 極大函數、恆等逼近、非切線收斂以及Calderon-Zygmund分解等四小節。第二個章節是在介紹A_p-權理論及其應用,而它包含了A_p-權理論及其在BMO空間上的應用兩小節。;In this thesis, we consider two chapters. Chapter 1 introduces the Hardy-Littlewood maximal function and its application. There are four sections including the Hardy-Littlewood maximal function, approimations of the identity, nontangential convergence, and the Calderon-Zygmund decomposition. Chapter 2 studies the A_p-weights theory and its application. There are two sections , the A_p-weights theory and the application to the BMO space.