实Hp空间四讲

Preface

Chapter 1 Real Variable Theory of Hp（R2） Spaces

1 Definition of Hp（Rn） spaces

2 Non-tangential maximal functions

3 Grand maximal functions

Chapter 2 Decomposition Structure Theory of Hp（Rn） Spaces

1 Atom

2 Dual space of H1（Rn）

3 Atom decomposition

4 Dual space of Hp（Rn）

5 Interpolation of operators

6 Interpolations of Hp spaces; weak Hp spaces

7 Molecule; molecule decomposition

8 Applications to the boundedness of operators

Chapter 3 Applications to Fourier Analysis

1 Fourier transform

2 The Fourier multiplier

3 The Riesz potential operators

4 Singular integral operators

5 The Bochner-Riesz means

6 Transference theorems of Hp multipliers

Chpater 4 Applications to Approximation Theory

1 K functional

2 HP multiplier and Jackson-type inequality

3 Hp multiplier and Bernstein type inequality

4 Approximation by Bochner-Riesz means at critical index

References

The whole book consists of four chapters. The basic theory of Fefferman-Stein on real Hp spaces is briefly introduced in Chapter 1. The contents in Chapter 2 involve the atomic decomposition theory and the molecular decomposition theory of real Hp spaces. In addition， the dual spaces of real Hp spaces， the interpolation of operators in Hp spaces， and the interpolation of Hp spaces are also discussed in Chapter 2 as a prerequisite for Chapters 3 and 4. The properties of several basic operators in Hp spaces will be discussed in Chapter 3 in detail. Among them， some basic results are contributed by Chinese mathematicians， such as the decomposition theory of weak Hp spaces and its applications to the study on the sharpness of singular integrals， a new method to deal with the elliptic Riesz means in Hp spaces， and the transference theorem of Hp multipliers， etc. The last chapter is devoted to applications of real HP spaces to approximation theory. The materials in Chapter 4 are fully contributed by Chinese mathematicians.