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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