《現代傅立葉分析（第3版）》是2017年8月1日世界圖書出版公司出版的著作，作者是[美] L.格拉法克斯。
基本介紹
- 書名：《現代傅立葉分析（第3版）》
- 作者：[美] L.格拉法克斯
- 出版社：世界圖書出版公司
- 出版時間：2017年08月01日
- ISBN：9787519226145
內容簡介,目錄,
內容簡介
《現代傅立葉分析（第3版 英文版）》旨在為讀者提供學習歐幾里得調和解析領域的理論基礎，各章有習題及提示。原始版本是以單卷集發布的，但是由於其體積、範圍和新材料的增加，第2版改為兩卷集發行，新增時頻分析和Carleson－Hunt定理等內容。
第3版在第2版的基礎上修訂新增一些章節，並將加權不等式一章從《現代傅立葉分析》調整到《經典傅立葉分析》，新增若干實例和套用內容，以及一些習題和提示。
目錄
1 Smoothness and Function Spaces
1．1 Smooth Functions and Tempered Distributions
1．1．1 Space of Tempered Distributions Modulo Polynomials
1．1．2 Calder6n Reproducing Formula
Exercises
1．2 Laplacian， Riesz Potentials， and Bessel Potentials
1．2．1 Riesz Potentials
1．2．2 Bessel Potentials
Exercises
1．3 Sobolev Spaces
1．3．1 Definition and Basic Properties of General Sobolev Spaces
1．3．2 Littlewood-Paley Characterization of Inhomogeneous
Sobolev Spaces
1．3．3 Littlewood-Paley Characterization of Homogeneous
Sobolev Spaces
Exercises
1．4 Lipschitz Spaces
1．4．1 Introduction to Lipschitz Spaces
1．4．2 Littlewood-Paley Characterization of Homogeneous
Lipschitz Spaces
1．4．3 Littlewood-Paley Characterization of Inhomogeneous
Lipschitz Spaces
Exercises
2 Hardy Spaces， Besov Spaces， and Triebel-Lizorkin Spaces
2．1 Hardy Spaces
2．1．1 Definition of Hardy Spaces
2．1．2 Quasi-norm Equivalence of Several Maximal Functions．．
2．1．3 Consequences of the Characterizations of Hardy Spaces．．
2．1．4 Vector-Valued Hp and Its Characterizations
2．1．5 Singular Integrals on vector-valued Hardy Spaces
Exercises
2．2 Function Spaces and the Square Function Characterization of Hardy
Spaces
2．2．1 Introduction to Function Spaces
2．2．2 Properties of Functions with Compactly Supported Fourier
Transforms
2．2．3 Equivalence of Function Space Norms
2．2．4 The Littlewood-Paley Characterization of Hardy Spaces ．．
Exercises
2．3 Atomic Decomposition of Homogeneous Triebel-Lizorkin
Spaces
2．3．1 Embeddings and Completeness of Triebel-Lizorkin Spaces
2．3．2 The Space of Triebel-Lizorkin Sequences
2．3．3 The Smooth Atomic Decomposition of Homogeneous
Triebel-Lizorkin Spaces
2．3．4 The Nonsmooth Atomic Decomposition of Homogeneous
Triebel-Lizorkin Spaces
2．3．5 Atomic Decomposition of Hardy Spaces
Exercises
2．4 Singular Integrals on Function Spaces
2．4．1 Singular Integrals on the Hardy Space H1
2．4．2 Singular Integrals on Besov-Lipschitz Spaces
2．4．3 Singular Integrals on HP（Rn）
2．4．4 A Singular Integral Characterization of H1 （Rn）
Exercises
3 BMO and Carleson Measures
3．1 Functions of Bounded Mean Oscillation
3．1．1 Definition and Basic Properties of BMO
3．1．2 The John-Nirenberg Theorem
3．1．3 Consequences of Theorem 3．1．6
Exercises
3．2 Duality between H1 and BMO
Exercises
3．3 Nontangential Maximal Functions and Carleson Measures
3．3．1 Definition and Basic Properties of Carleson Measures
3．3．2 BMO Functions and Carleson Measures
Exercises
3．4 The Sharp Maximal Function
3．4．1 Definition and Basic Properties of the Sharp Maximal
Function
3．4．2 A Good Lambda Estimate for the Sharp Function
……
