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.

References

[1] J. Duoandikoetxea, Fourier analysis, Translated and revised from the 1995 Spanish original by David Cruz-Uribe. Graduate Studies in Mathematics, 29. American Mathematical Society, Providence, RI, 2001.
[2] E.M.Stein, Singular integrals and differentiability properties of functions. Princeton Mathematical Series, No. 30 Princeton University Press, Princeton, N.J. 1970.
[3] R.L. Wheeden; A. Zygmund, Measure and integral. An introduction to real analysis. Pure and Applied Mathematics, Vol. 43. Marcel Dekker, Inc., New York-Basel,1977.
[4] 林欽誠，調和分析，現代數學基礎59，北京高等教育出版社，2016。
[5] 韓永生，近代調和分析方法及其應用，現代數學基礎叢書，科學出版社，1997。