Muscalu C., Schlag W. Classical and multilinear harmonic analysis. Volume 2

Cambridge University Press, 2013. — 342 p. — (Cambridge Studies in Advanced Mathematics 138) — ISBN: 1107031826This 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.Leibnitz rules and the generalized Korteweg–de Vries equation
Classical paraproducts
Paraproducts on polydisks
Calderón commutators and the Cauchy integral on Lipschitz curves
Iterated Fourier series and physical reality
The bilinear Hilbert transform
Almost everywhere convergence of Fourier series
Flag paraproducts
Appendix: Multilinear interpolation