Classical and Multilinear Harmonic Analysis

摘要: This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained will be useful to graduate students researchers both pure applied analysis. Numerous exercises problems make the suitable for self-study classroom alike. first volume starts with classical one-dimensional topics: Fourier series; functions; Hilbert transform. Then higher-dimensional Calderon–Zygmund Littlewood–Paley theories are developed. Probabilistic methods their applications discussed, as partial differential equations. The concludes an introduction Weyl calculus. second goes beyond highly contemporary focuses on multilinear aspects analysis: bilinear transform; Coifman–Meyer theory; Carleson's resolution Lusin conjecture; Calderon's commutators Cauchy integral Lipschitz curves. material this has not previously appeared together book form.