经典傅里叶分析 : 第2版

The Riesz-Thorin Interpolation Theorem.

1.3.3 Interpolation of Analytic Families of Operators

1.3.4 Proofs of Lemmas 1.3.5 and 1.3.8

Exercises

1.4 Lorentz Spaces

1.4.1 Decreasing Rearrangements

1.4.2 Lorentz Spaces

1.4.3 Duals of Lorentz Spaces

1.4.4 The Off-Diagonal Marcinkiewicz Interpolation Theorem

Exercises

2 Maximal Functions, Fourier Transform, and Distributions

2.1 Maximal Functions

2.1.1 The Hardy-Littlewood Maximal Operator

2.1.2 Control of Other Maximal Operators

2.1.3 Applications to Differentiation Theory

Exercises

2.2 The Schwartz Class and the Fourier Transform

2.2.1 The Class of Schwartz Functions

2.2.2 The Fourier Transform of a Schwartz Function

2.2.3 The Inverse Fourier Transform and Fourier Inversion

2.2.4 The Fourier Transform on L1+L2

Exercises

2.3 The Class of Tempered Distributions

2.3.1 Spaces of Test Functions

2.3.2 Spaces of Functionals on Test Functions

2.3.3 The Space of Tempered Distributions

2.3.4 The Space of Tempered Distributions Modulo Polynomials.

Exercises

2.4 More About Distributions and the Fourier Transform

2.4.1 Distributions Supported at a Point

2.4.2 The Laplacian

2.4.3 Homogeneous Distributions

Exercises

2.5 Convolution Operators on LP Spaces and Multipliers

2.5.1 Operators That Commute with Translations

2.5.2 The Transpose and the Adjoint of a Linear Operator

2.5.3 The Spaces.

2.5.4 Characterizations

2.5.5 The Space of Fourier Multipliers

Exercises

2.6 Oscillatory Integrals

2.6.1 Phases with No Critical Points

2.6.2 Sublevel Set Estimates and the Van der Corput Lemma

Exercises

……

3 Fourier Analysis on the Torus

4 Singular Integrals of Convolution Type

5 Littlewood-Paley Theory and Multipliers

《经典傅里叶分析(第2版)(英文)》由世界图书出版公司北京公司出版。《经典傅里叶分析(第2版)(英文)》内容丰富，全书中两卷集的作品旨在为读者提供学习欧几里得调和解析领域的理论基础。原始版本是以单卷集发布的，但是由于其体积、范围和新材料的增加，第二版改为两卷集发行。【作者简介】作者：（美国）格拉法克斯（Loukas Grafakos）