Weighted Littlewood-Paley Theory and Exponential-Square IntegrabilitySpringer, 31 dec. 2007 - 227 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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... norm defined by f4≡ (∫ |f(x)|4dx ) 1/4. To make things specific, let's suppose that our functions are defined on ... Lp, the Lp norms of S(f) and f are comparable. The combination of these two facts—domination plus comparablility—lets ...
... norm inequalities. The reader will learn some sufficient (and not terribly ... norm inequalities) imply that this connection is pretty close. We have tried to ... Lp(w) for w ∈ Ap and we prove an extrapolation result—because we need both ...
... Lp spaces for 1 ≤ p ≤ ∞) provides a flexible way of keeping track of the integrability properties of functions. It is very useful in the study of weighted norm inequalities. The material here could have come at the very beginning ...
... Lp (p = 2) and so-called weighted spaces, in which the underlying measure is no longer the familiar Lebesgue one. For example, it turns out that, if 1 <p< ∞, there are constants cp and Cp so that, for all f∈ Lp ... norm means different ...
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Cuprins
1 | |
9 | |
Exponential Square 39 | 38 |
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 Goodλ | 189 |
A Fourier Multiplier Theorem | 197 |
VectorValued Inequalities | 203 |
Random Pointwise Errors | 213 |
References | 219 |
Index 223 | 222 |
Some Singular Integrals | 151 |
Alte ediții - Afișează-le pe toate
Weighted Littlewood-Paley Theory and Exponential-Square ..., Ediția 1924 Michael Wilson Previzualizare limitată - 2008 |