《實Hp空間四講》是一本專著， 它介紹了Hp空間的實變理論及其在分析領域中的套用。全書分四章。第一章以簡短的篇幅介紹了Hp空間的Fefferman—Stein理論， 這個理論的核心是用多種形式的極大函式來刻畫Hp空間的特徵；第二章是建立Hp空間的分解結構理論， 其中包括Coifman的原子分解理論和Taibleson—Weiss的分子分解理論；第三章是作為前兩章內容的套用， 研究了分析領域中若干基本運算元在Hp空間上的有界性質；第四章運用頭兩章中的理論並結合乘子理論， 系統地建立了Hp空間上的逼近理論， 包括逼近的正定理和逆定理。
基本介紹
- 書名：實Hp空間四講
- 作者：陸 (Lu.S.)
- 出版日期：2008年8月1日
- 語種：英語
- ISBN：9787506291842
- 外文名：Four Lectures on Real Hp Spaces
- 出版社：世界圖書出版公司北京公司
- 頁數：217頁
- 開本：24
- 品牌：世界圖書出版公司北京公司
基本介紹,內容簡介,作者簡介,圖書目錄,序言,
基本介紹
內容簡介
《實Hp空間四講》可用作為數學專業研究生教材， 也可供相關專業的研究工作者參考。
作者簡介
作者：(德國)陸 (Lu.S.)
圖書目錄
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
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
序言
It is well known that the study on Hp spaces has been going on for a long period. The classical Hp spaces on the unit circle or upper half-plane are defined by the aid of complex method. The theory of these spaces plays an important role in the study of the classical Fourier analysis. It is natural to extend the definitions of these spaces to higher dimensional case along with the development of the Fourier analysis on Euclidean spaces. The first work on this was done by E. M. Stein and G. Weiss. The definition and theory of the n-dimensional Hp spaces that they established in the early days of the sixties are based on the method of harmonic functions instead of the complex method. However, the most important step in the development of Hp spaces is that the real variable theory of Hp spaces was found by virtue of the method of maximal functions in the early days of the seventies. The purpose of this book is to introduce the real variable theory of Hp spaces in short and pay more attention to its applications to some respects in analysis fields.
The whole book consists of four chapters. The basic theory of FeffermanStein 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.
The whole book consists of four chapters. The basic theory of FeffermanStein 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.
