9781107031821

Classical and Multilinear Harmonic Analysis

  • ISBN 13:

    9781107031821

  • ISBN 10:

    1107031826

  • Format: Hardcover
  • Copyright: 03/31/2013
  • Publisher: Cambridge Univ Pr

Note: Not guaranteed to come with supplemental materials (access cards, study guides, lab manuals, CDs, etc.)

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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.

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