LEADER 05704nam 22007332 450 001 9910815215003321 005 20160525165355.0 010 $a1-139-61116-X 010 $a1-107-23788-2 010 $a1-139-61302-2 010 $a1-139-62232-3 010 $a1-283-94327-1 010 $a1-139-62604-3 010 $a1-139-60934-3 010 $a1-139-41039-3 010 $a1-139-61674-9 035 $a(CKB)2670000000326640 035 $a(EBL)1099945 035 $a(OCoLC)823724196 035 $a(SSID)ssj0000877948 035 $a(PQKBManifestationID)11460740 035 $a(PQKBTitleCode)TC0000877948 035 $a(PQKBWorkID)10812465 035 $a(PQKB)10514396 035 $a(UkCbUP)CR9781139410397 035 $a(Au-PeEL)EBL1099945 035 $a(CaPaEBR)ebr10643410 035 $a(CaONFJC)MIL425577 035 $a(MiAaPQ)EBC1099945 035 $a(PPN)261294431 035 $a(EXLCZ)992670000000326640 100 $a20120417d2013|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aClassical and multilinear harmonic analysis$hVolume 2 /$fCamil Muscalu, Wilhelm Schlag$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2013. 215 $a1 online resource (xvi, 324 pages) $cdigital, PDF file(s) 225 1 $aCambridge studies in advanced mathematics ;$v138 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a1-107-47153-2 311 $a1-107-03182-6 320 $aIncludes bibliographical references and index. 327 $aContents; Preface; Acknowledgements; 1 Leibnitz rules and the generalized Korteweg-de Vries equation; 1.1 Conserved quantities; 1.2 Dispersive estimates for the linear equation; 1.3 Dispersive estimates for the nonlinear equation; 1.4 Wave packets and phase-space portraits; 1.5 The phase-space portraits of e2ix2 and e2ix3; 1.6 Asymptotics for the Airy function; Notes; Problems; 2 Classical paraproducts; 2.1 Paraproducts; 2.2 Discretized paraproducts; 2.3 Discretized Littlewood-Paley square-function operator; 2.4 Dualization of quasi-norms; 2.5 Two particular cases of Theorem 2.3 327 $a3.7 Proof of Theorem 3.1 part 2; 3.8 Multiparameter paraproducts; 3.9 Proof of Theorem 3.1; a simplification; 3.10 Proof of the generic decomposition; Notes; Problems; 4 Calder ?on commutators and the Cauchy integral; 4.1 History; 4.2 The first Calder ?on commutator; 4.3 Generalizations; 4.4 The Cauchy integral on Lipschitz curves; 4.5 Generalizations; Notes; Problems; 5 Iterated Fourier series and physical reality; 5.1 Iterated Fourier series; 5.2 Physical reality; 5.3 Generic Lp AKNS systems for 1p < 2; 5.4 Generic L2 AKNS systems; Notes; Problems; 6 The bilinear Hilbert transform 327 $a6.1 Discretization6.2 The particular scale-1 case of Theorem 6.5; 6.3 Trees, L2 sizes, and L2 energies; 6.4 Proof of Theorem 6.5; 6.5 Bessel-type inequalities; 6.6 Stopping-time decompositions; 6.7 Generic estimate of the trilinear BHT form; 6.8 The 1/2 < r < 2/3 counterexample; 6.9 The bilinear Hilbert transform on polydisks; Notes; Problems; 7 Almost everywhere convergence of Fourier series; 7.1 Reduction to the continuous case; 7.2 Discrete models; 7.3 Proof of Theorem 7.2 in the scale-1 case; 7.4 Estimating a single tree; 7.5 Additional sizes and energies; 7.6 Proof of Theorem 7.2 327 $a7.7 Estimates for Carleson energies7.8 Stopping-time decompositions; 7.9 Generic estimate of the bilinear Carleson form; 7.10 Fefferman's counterexample; Notes; Problems; 8 Flag paraproducts; 8.1 Generic flag paraproducts; 8.2 Mollifying a product of two paraproducts; 8.3 Flag paraproducts and quadratic NLS; 8.4 Flag paraproducts and U-statistics; 8.5 Discrete operators and interpolation; 8.6 Reduction to the model operators; 8.7 Rewriting the 4-linear forms; 8.8 The new size and energy estimates; 8.9 Estimates for T1 and T1,l0 near A4; 8.10 Estimates for T1*3 and T*31,l0 near A31 and A32 327 $a8.11 Upper bounds for flag sizes 330 $aThis two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and useful to graduates and researchers in pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. The first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Caldero?n-Zygmund and Littlewood-Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman-Meyer theory; Carleson's resolution of the Lusin conjecture; Caldero?n's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form. 410 0$aCambridge studies in advanced mathematics ;$v138. 517 3 $aClassical & Multilinear Harmonic Analysis 606 $aHarmonic analysis 615 0$aHarmonic analysis. 676 $a515/.2422 700 $aMuscalu$b Camil$0480408 702 $aSchlag$b Wilhelm$f1969- 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910815215003321 996 $aClassical and multilinear harmonic analysis$94003722 997 $aUNINA