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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... results (and the corresponding weighted norm inequalities) imply that this connection is pretty close. We have tried to ... result—because we need both—but we don't prove Ap factorization or the Rubio de Francia extrapolation theorem ...
... results of the preceding chapters to d dimensions and to continuous analogues of the dyadic square function. Chapters 5, 6, and 7 are devoted to the Calderón reproducing formula. The Calderón formula provides a canonical way of ...
... results. In this section I will try to acquaint the reader with what things are taken for granted in weighted LittlewoodPaley theory. Some of these things are definitions and notations, and some of them are theorems. We assume that the ...
... result 2.2, which says that f2 = S(f)2 (2.9) for f ∈ L2. Before going one step further, it will be profitable to reflect on the meaning of 2.9. It is a peculiar equation. Let's first consider f2 ≤ S(f)2. (2.10) Notice that |f| 2 ...
... results. The first OIle IS //ølo" fol/l)" /M (nar (2.1% I I The second result is # | (Ma(f))” dr & Co (# | |f| *). (2.16) valid for 0 < 3 < 1. Inequality 2.15 says that, if we restrict our attention to an interval, then Ma(f) is ...
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 |