几类与Heisenberg群相关的函数空间和变分问题研究

摘要

该文的主要目的是系统研究靶流形为Heisenberg群的函数及其空间的性质.另外我们还研究了Heisenberg群上一类半线性次调和方程的解的存在性问题及Heisenberg上群一类次调和算子的特征值估计问题.部分结果是作者对欧氏空间中相关问题研究成果的推广.

目录

文摘

英文文摘

CHAPTER O INTRODUCTION

CHAPTER 1 THE HEISENBERG GROUP AND THE MAPS FOR THE GROUP TARGETS

§1.1 THE CONSTRUCTION OF HEISENBERG GROUP Hn

§1.2 THE BASIC PROPERTIES OF THE HEISENBERG GROUP (Hn, d)

§1.3 THE LIPSCHITZ MAPS FOR THE HEISENBERG GROUP TARGETS

CHAPTER 2 Lp(Ω, Hn), W1,p(Ω, Hn) and BMO(Ω,Hn)

2.1 THE DEFINITION AND THE BASIC PROPERTIES OF Lp(Ω, Hn)

2.2 THE DEFINITIONS AND THE BASIC PROPERTIES OF W1,p(Ω, Hn)

2.3 THE PRE-NORM AND PRE-WEAKLY COMPACTNESS ON W1,p(Ω, Hn)

2.4 BMO SPACES AND JOHN-NIRENBERG ESTIMATES FOR THE HEISENBERG GROUP TARGETS

CHAPTER 3 POINCARE INEQUALITIES AND REVERSE POINCARE INEQUALITIES IN W1,p(Ω, Hn)

3.1 THE POINCARE INEQUALITIES

5.1 THE EXISTENCE OF THE MINIMIZERS

5.2 THE EULER EQUATIONS AND THE APPROXIMATIONS FOR THE MINIMIZERS

CHAPTER 6 EXISTENCE OF THE SOLUTIONS TO THE SEMILINEAR EQUATIONS AND ESTIMATES OF THE EIGENVALUES ON THE HEISENBERG GROUP

6.1 EXISTENCE OF THE SOLUTIONS FOR THE SEMILINEAR SUBELLIPTIC EQUATIONS ON THE HEISENBERG GROUP

6.2 ESTIMATIONS OF THE EIGENVALUES FOR THE SUBELLIPTIC OPERATORS ON THE HEISENBERG GROUP

Acknowledgements

References

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