Classical and Multilinear Harmonic Analysis

by Muscalu, Camil; Schlag, Wilhelm

• ISBN13: 9781107031821
• ISBN10: 1107031826
• Format: Hardcover
• Copyright: 2013-03-31
• Publisher: Cambridge Univ Pr

Summary

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 Calderon-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; Calderon's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form.

Table of Contents

Preface

Acknowledgements

Leibniz rules and gKdV equations

Classical paraproducts

Paraproducts on polydiscs

Calderón commutators and the Cauchy integral

Iterated Fourier series and physical reality

The bilinear Hilbert transform

Almost everywhere convergence of Fourier series

Flag paraproducts

Appendix: multilinear interpolation

Bibliography

Index

Table of Contents provided by Publisher. All Rights Reserved.