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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... space for a given problem. We might want to work in L4, with its norm defined by 1/4 f 4 ≡ (∫ |f(x)| ) 4 dx . To ... Lp, the Lp norms of S(f) and f are comparable. The combination of these two facts—domination plus comparablility ...
... spaces (which in- cludes that of 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 ...
... Lebesgue integral ( in 1 and d dimensions ) , LP spaces in Rd ( 1 ≤ p ≤ ∞ ) and their duals , and some functional analysis . We also assume that the reader knows a little about the Fourier transform . We will use certain definitions ...
... LP spaces , and even to weighted LP spaces ? ( We'll explain what weighted spaces are in a bit . ) To put it more generally : When can we use a vector - space decomposition of a function, via Haar functions, to get information 12 2 An ...
... LP ( p2 ) 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 fe LP ( R ) , Cp || f ...
Cuprins
1 | |
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 |
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 |