LEADER 06180nam 22007332 450 001 9910817544503321 005 20160526163425.0 010 $a1-107-23372-0 010 $a1-139-60986-6 010 $a1-139-61172-0 010 $a1-139-62102-5 010 $a1-283-94313-1 010 $a1-139-62474-1 010 $a1-139-61544-0 010 $a1-139-60838-X 010 $a1-139-04708-6 035 $a(CKB)2670000000324853 035 $a(EBL)1099818 035 $a(OCoLC)823724583 035 $a(SSID)ssj0000877947 035 $a(PQKBManifestationID)11455184 035 $a(PQKBTitleCode)TC0000877947 035 $a(PQKBWorkID)10829083 035 $a(PQKB)10183305 035 $a(UkCbUP)CR9781139047081 035 $a(Au-PeEL)EBL1099818 035 $a(CaPaEBR)ebr10643422 035 $a(CaONFJC)MIL425563 035 $a(MiAaPQ)EBC1099818 035 $a(PPN)261276271 035 $a(EXLCZ)992670000000324853 100 $a20110304d2013|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aClassical and multilinear harmonic analysis$hVolume 1 /$fCamil Muscalu, Wilhelm Schlag$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2013. 215 $a1 online resource (xviii, 370 pages) $cdigital, PDF file(s) 225 1 $aCambridge studies in advanced mathematics ;$v137 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a1-107-47159-1 311 $a0-521-88245-1 320 $aIncludes bibliographical references and index. 327 $aContents; Preface; Acknowledgements; 1 Fourier series: convergence and summability; 1.1 The basics: partial sums and the Dirichlet kernel; 1.2 Approximate identities, Fej ?er kernel; 1.3 The Lp convergence of partial sums; 1.4 Regularity and Fourier series; 1.5 Higher dimensions; 1.6 Interpolation of operators; Notes; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; 2 Harmonic functions; Poisson kernel; 2.1 Harmonic functions; 2.2 The Poisson kernel; 2.3 The Hardy-Littlewood maximal function 327 $a2.4 Almost everywhere convergence2.5 Weighted estimates for maximal functions; Notes; 3 Conjugate harmonic functions; Hilbert transform; 3.1 Hardy spaces of analytic functions; 3.2 Riesz theorems; 3.3 Definition and simple properties of the conjugate function; 3.4 The weak-L1 bound on the maximal function; 3.5 The Hilbert transform; 3.6 Convergence of Fourier series in Lp; Notes; 4 The Fourier transform on Rd and on LCA groups; 4.1 The Euclidean Fourier transform; 4.2 Method of stationary or nonstationary phases; 4.3 The Fourier transform on locally compact Abelian groups; Notes 327 $a5 Introduction to probability theory5.1 Probability spaces; independence; 5.2 Sums of independent variables; 5.3 Conditional expectations; martingales; Notes; 6 Fourier series and randomness; 6.1 Fourier series on L1(T): pointwise questions; 6.2 Random Fourier series: the basics; 6.3 Sidon sets; Notes; 7 Calder ?on-Zygmund theory of singular integrals; 7.1 Calder ?on-Zygmund kernels; 7.2 The Laplacian: Riesz transforms and fractional integration; 7.3 Almost everywhere convergence; homogeneous kernels; 7.4 Bounded mean oscillation space; 7.5 Singular integrals and Ap weights 327 $a7.6 A glimpse of H1-BMO duality and further remarksNotes; 8 Littlewood-Paley theory; 8.1 The Mikhlin multiplier theorem; 8.2 Littlewood-Paley square-function estimate; 8.3 Calderon-Zygmund H ?older spaces, and Schauder estimates; 8.4 The Haar functions; dyadic harmonic analysis; 8.5 Oscillatory multipliers; Notes; 9 Almost orthogonality; 9.1 Cotlar's lemma; 9.2 Calderon-Vaillancourt theorem; 9.3 Hardy's inequality; 9.4 The T(1) theorem via Haar functions; 9.5 Carleson measures, BMO, and T(1); Notes; 10 The uncertainty principle; 10.1 Bernstein's bound and Heisenberg's uncertainty principle 327 $a10.2 The Amrein-Berthier theorem10.3 The Logvinenko-Sereda theorem; 10.4 Solvability of constant-coefficient linear PDEs; Notes; 11 Fourier restriction and applications; 11.1 The Tomas-Stein theorem; 11.2 The endpoint; 11.3 Restriction and PDE; Strichartz estimates; 11.4 Optimal two-dimensional restriction; Notes; 12 Introduction to the Weyl calculus; 12.1 Motivation, definitions, basic properties; 12.2 Adjoints and compositions; 12.3 The L2 theory; 12.4 A phase-space transform; Notes; References; Index 330 $aThis two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. This first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Caldero?n-Zygmund and Littlewood-Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman-Meyer theory; Carleson's resolution of the Lusin conjecture; Caldero?n's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form. 410 0$aCambridge studies in advanced mathematics ;$v137. 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 $a9910817544503321 996 $aClassical and multilinear harmonic analysis$94003722 997 $aUNINA