LEADER 03648nam a2200397 i 4500 001 991002667559707536 008 141218s2013 enka b 001 0 eng 020 $a9780521882453 (v. 1 : hardback) 020 $a0521882451 (v. 1 : hardback) 020 $a9781107031821 (v. 2 : hardback) 020 $a1107031826 (v. 2 : hardback) 020 $a1107032628 (set) 035 $ab14213187-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a515.2422$223 084 $aAMS 42-02 084 $aLC QA403$b.M87 100 1 $aMuscalu, Camil$0480408 245 10$aClassical and multilinear harmonic analysis /$cCamil Muscalu, Wilhelm Schlag 260 $aCambridge, UK :$bCambridge University Press,$c2013 300 $a2 v. :$bil. ;$c24 cm 440 0$aCambridge studies in advanced mathematics ;$v137-138 504 $aIncludes bibliographical references and indexes 505 0 $av.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 ; Calderón-Zygmund theory of singular integrals ; Littlewood-Paley theory ; Almost orthogonality ; The uncertainty principle ; Fourier restriction and applications ; Introduction to the Weyl calculus 505 0 $av. 2.: 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 520 $a"This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained, and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. This first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón-Zygmund and Littlewood-Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary, and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman-Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form": Provided by publisher 650 0$aHarmonic analysis 700 1 $aSchlag, Wilhelm$eauthor$4http://id.loc.gov/vocabulary/relators/aut$0521272 856 42$zCover image$uhttp://assets.cambridge.org/97805218/82453/cover/9780521882453.jpg 907 $a.b14213187$b16-03-15$c30-01-15 912 $a991002667559707536 945 $aLE013 42-XX MUS11 V.I (2013)$cV. 1$g1$i2013000292762$lle013$op$pE50.50$q-$rl$s- $t0$u1$v0$w1$x0$y.i15661696$z16-03-15 945 $aLE013 42-XX MUS11 V.II (2013)$cV. 2$g1$i2013000292779$lle013$o-$pE50.51$q-$rl$s- $t0$u1$v0$w1$x0$y.i15661702$z16-03-15 996 $aClassical and multilinear harmonic analysis$9833206 997 $aUNISALENTO 998 $ale013$b18-12-14$cm$da $e-$feng$genk$h0$i0