Weighted Littlewood-Paley Theory and Exponential-Square Integrability, Ediția 1924Springer Science & Business Media, 2008 - 224 pagini Littlewood-Paley theory is an essential tool of Fourier analysis, with applications and connections to PDEs, signal processing, and probability. It extends some of the benefits of orthogonality to situations where orthogonality doesn’t really make sense. It does so by letting us control certain oscillatory infinite series of functions in terms of infinite series of non-negative functions. Beginning in the 1980s, it was discovered that this control could be made much sharper than was previously suspected. The present book tries to give a gentle, well-motivated introduction to those discoveries, the methods behind them, their consequences, and some of their applications. |
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Pagina ix
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Cuprins
Some Assumptions | 1 |
An Elementary Introduction | 9 |
Exponential Square 39 | 40 |
Many Dimensions Smoothing | 69 |
The Calderón Reproducing Formula I | 85 |
The Calderón Reproducing Formula II | 101 |
The Calderón Reproducing Formula III | 129 |
Schrödinger Operators 145 | 144 |
Orlicz Spaces | 161 |
Goodbye to GoodX | 189 |
A Fourier Multiplier Theorem | 197 |
VectorValued Inequalities | 203 |
Random Pointwise Errors | 213 |
219 | |
222 | |
Some Singular Integrals | 151 |
Alte ediții - Afișează-le pe toate
Weighted Littlewood-Paley Theory and Exponential-Square Integrability Michael Wilson Previzualizare limitată - 2007 |
Termeni și expresii frecvente
adapted functions argument assume belong bounded Calderón formula Calderón reproducing formula chapter Chebyshev's inequality compact-measurable exhaustion converges Corollary cubes Q defined definition denote depending dt dy dyadic cubes dyadic doubling dyadic square function dµ(x equal equation estimate everywhere exercise finishes the proof finite linear sums finite sums functions ƒ Haar functions Hardy-Littlewood maximal Hardy-Littlewood maximal function Hölder inequality holds implies Lebesgue Lebesgue measure Let f Littlewood-Paley theory Lº(w locally integrable log(e Lp norm LP spaces Ma(v Martina Franca maximal function maximal operator measurable function measure space non-negative Orlicz maximal Orlicz space pointwise positive constant positive numbers Proof of Theorem R+¹ Rademacher function radial Rd+1 reader satisfies sequence subset sums of Haar support contained Suppose supremum Theorem 2.1 yields Young function