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Classical and Multilinear Harmonic Analysis.
This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2013.
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| Colección: | Cambridge studies in advanced mathematics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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. 2.6 The John
- Nirenberg inequality2.7 L1" sizes and L1" energies; 2.8 Stopping-time decompositions; 2.9 Generic estimate of the trilinear paraproduct form; 2.10 Estimates for sizes and energies; 2.11 Lp bounds for the first discrete model; 2.12 Lp bounds for the second discrete model; 2.13 The general Coifman-Meyer theorem; 2.14 Bilinear pseudodifferential operators; Notes; Problems; 3 Paraproducts on polydisks; 3.1 Biparameter paraproducts; 3.2 Hybrid square and maximal functions; 3.3 Biparameter BMO; 3.4 Carleson's counterexample; 3.5 Proof of Theorem 3.1; part 1; 3.6 Journ ́e's lemma. 3.7 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. 6.1 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. 7.7 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. 8.11 Upper bounds for flag sizes.