Download Classical and Multilinear Harmonic Analysis: 1 (Cambridge by Camil Muscalu,Wilhelm Schlag PDF

By Camil Muscalu,Wilhelm Schlag

This two-volume textual content in harmonic research introduces a wealth of analytical effects and strategies. it truly is principally self-contained and may be beneficial to graduate scholars and researchers in either natural and utilized research. various routines and difficulties make the textual content appropriate for self-study and the school room alike. this primary quantity starts off with classical one-dimensional themes: Fourier sequence; harmonic features; Hilbert rework. Then the higher-dimensional Calderón–Zygmund and Littlewood–Paley theories are built. Probabilistic equipment and their functions are mentioned, as are functions of harmonic research to partial differential equations. the amount concludes with an creation to the Weyl calculus. the second one quantity is going past the classical to the hugely modern and makes a speciality of multilinear features of harmonic research: the bilinear Hilbert remodel; Coifman–Meyer conception; Carleson's answer of the Lusin conjecture; Calderón's commutators and the Cauchy fundamental on Lipschitz curves. the cloth during this quantity has now not formerly seemed jointly in booklet form.

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