Classical and multilinear harmonic analysis - Muscalu, Camil; Schlag, Wilhelm (Cambridge, UK Cambridge University Press, 2013)
v.1. Fourier series: convergence and summability ; Harmonic functions; Poisson kernel ; Conjugate harmonic fuctions; Hilbert transform ; The Fourier transform on R[superscript d] and on LCA groups ; Introduction to probability theory ; Fourier series and randomness ; Calderâon-Zygmund theory of singular integrals ; Littlewood-Paley theory ; Almost orthogonality ; The uncertainty principle ; Fourier restriction and applications ; Introduction to the Weyl calculus -- v. 2. Leibnitz rules and the generalized Korteweg-de Vries equation ; Classical paraproducts ; Paraproducts on polydisks ; Calderâon 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.
Includes bibliographical references and index.
Keywords: Harmonic analysis