9781107031821

Classical and Multilinear Harmonic Analysis

by ;
  • ISBN13:

    9781107031821

  • ISBN10:

    1107031826

  • Format: Hardcover
  • Copyright: 3/31/2013
  • Publisher: Cambridge Univ Pr
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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.

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