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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... reader will encounter two conventions, endemic in Fourier analysis, which he might find a little disturbing. They are “the constantly changing constant”1 and the use of '∼'. Much of analysis is about proving inequalities. We have two ...
... reader should check this. A more interesting example is given by A(t)=t/(log(e.-- t))” and B(t) = the inverse function of t(log(e.-- t))"—and the reader should check this one, too. Unless we are very interested in the values of C1 and ...
... reader could reasonably ask what purpose is served by being able to split f this way for every positive A. Why isn't it enough to split it just for X = 1? That is another story that will have to wait. Notes The Calderón-Zygmund ...
... reader should satisfy himself of the truth of the following statement: If I e D and I Z [0,1), then X1(f) = 0. This says that the sum XE, AI(f)h(1) is, in a very useful sense, localized. For, suppose now that f is an arbitrary locally ...
... reader should see for himself that XI (fi) if I C [0, 1); XI (f) = { \' Otherwise. and that, in fact, if J is any dyadic interval, and we split f into f1 + f2, where ("-" if a € J: 0 Otherwise, fi(a)= we will have J XI (fi) if I C J, AI ...
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 |