Classical and Multilinear Harmonic Analysis : Volume 2

基本信息

Series:Cambridge Studies in Advanced Mathematics

Format:Hardback 339 pages, Worked examples or Exercises; 15 Line drawings, unspecified

Publisher:Cambridge University Press

Imprint:Cambridge University Press

ISBN:9781107031821

Published: 31 Jan 2013

Classifications:Real analysis, real variables, Complex analysis, complex variables, Differential calculus & equations, Integral calculus & equations

Readership:Tertiary Education (US: College)

Weight:624g

Dimensions:235 x 157 x 22 (mm)

Pub. Country:United Kingdom

页面参数仅供参考，具体以实物为准

书籍简介

《谐波分析》的两卷本介绍了大量的分析结果和技术。在纯分析和应用分析方面，它在很大程度上是独立的，对毕业生和研究人员有用。本课程的作业和问题适合学生自主学习和课堂学习。第一卷从经典的一维主题开始:傅里叶级数;调和函数;希尔伯特变换。在更高维度上，形成了齐格蒙德和利特尔伍德-佩利理论。本书还讨论了非概率方法及其应用，以及谐波分析在偏微分方程中的应用。卷以韦尔微积分的介绍结束。第二卷超越了经典，转向高度现代，关注谐波分析的多线性方面:双线性希尔伯特变换;Coifman-Meyer理论;Carleson对Lusin猜想的解答;卡尔德龙对易子和利普希茨曲线上的柯西积分。本卷中的材料以前并没有以书的形式一起出现。

This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and useful to graduates and researchers in pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. The first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón–Zygmund and Littlewood–Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman–Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form.

目录

Preface

Acknowledgements

1. Leibniz rules and gKdV equations

2. Classical paraproducts

3. Paraproducts on polydiscs

4. Calderón commutators and the Cauchy integral

5. Iterated Fourier series and physical reality

6. The bilinear Hilbert transform

7. Almost everywhere convergence of Fourier series

8. Flag paraproducts

9. Appendix: multilinear interpolation

Bibliography

Index

作者简介

Camil Muscalu是纽约康奈尔大学的数学副教授。

威廉·施拉格(Wilhelm Schlag)是芝加哥大学数学系教授。

Camil Muscalu is Associate Professor of Mathematics at Cornell University, New York.

Wilhelm Schlag is Professor in the Department of Mathematics at the University of Chicago.