海森堡群在量子物理学和许多数学领域, 包括傅里叶分析、复变函数、几何和拓扑中发挥了重要作用. 本文在海森堡群中引入了Musielak-Orlicz空间, 并在此空间中对Muckenhoupt权Aq进行了推广, 且对此推广做了进一步研究. 具体内容如下：
第一章是背景知识和主要结论, 主要介绍了Orlicz空间, Muckenhoupt权Aq和分数次积分算子的发展历程和研究意义, 同时简单地介绍了本篇论文的主要工作.
在第二章中, 首先给出了本征N函数的定义及其性质. 在此基础上, 引入了Musielak-Orlicz空间以及Musielak-Orlicz序列空间, 且通过对Muckenhoupt权Aq的推广, 引入了ClassA的定义.
在第三章中, 借助函数间的控制关系, 我们找到了有关ClassA 的等价关系, 即对ClassA的刻画, 并给出了有关N函数的一些结果.
另外, 在调和分析中, 分数次积分算子在经典Lebesgue空间上的有界性是重点研究对象之一, 本文将在第四章中证明海森堡群上多线性分数次积分算子在变指数Lebesgue空间上的有界性.

The Heisenberg group plays an important role in quantum physics and many fields of mathematics, including Fourier analysis, functions of several complex variables, geometry, and topology. In this paper, we will introduce Musielak-Orlicz spaces into Heisenberg group, and generalize the concept of Muckenhoupt classes to this spaces, on which we will do some further research. The details are as follows:
The background and the main conclusions are given in the first chapter. We mainly introduce the process of the development and the significance of the research for Orlicz spaces，Muckenhoupt classes Aq and fractional integral operators. At the same time, the main works of this paper are explained briefly.
In the second chapter, firstly, the definition and properties of N-function are given. On this basis, we'll introduce Musielak-Orlicz spaces and Musielak-Orlicz sequence spaces. By generalizing the concept of Muckenhoupt classes to Musielak-Orlicz spaces, we introduce the definition of Class A.
In the third chapter, under the control relationship between some functions, we have worked out some equivalence relationship for Class A，which is an alternative characterization of Class A. We also give some results of N-function.
Moreover, in the field of harmonic analysis, it is focused on the study of the boundedness of fractional integral operators on the classical Lebesgue spaces. In Chapter 4, we will prove the boundedness of multilinear fractional integral operators on the variable exponent Lebesgue spaces on Heisenberg group.