实HP空间四讲（英文版） 下载 pdf 百度网盘 epub 免费 2025 电子书 mobi 在线

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.

Preface

Chapter 1 Real Variable Theory of Hp(Rn) 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 Hr spaces; weak Hr 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-Piesz means at critical index

References

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书籍介绍

《实Hp空间四讲》是一本专著， 它介绍了Hp空间的实变理论及其在分析领域中的应用。全书分四章。第一章以简短的篇幅介绍了Hp空间的Fefferman—Stein理论， 这个理论的核心是用多种形式的极大函数来刻画Hp空间的特征；第二章是建立Hp空间的分解结构理论， 其中包括Coifman的原子分解理论和Taibleson—Weiss的分子分解理论；第三章是作为前两章内容的应用， 研究了分析领域中若干基本算子在Hp空间上的有界性质；第四章运用头两章中的理论并结合乘子理论， 系统地建立了Hp空间上的逼近理论， 包括逼近的正定理和逆定理。