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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... case. Another way to consider 2.9 is in terms of energy and amplitude. Think ... inequality like 2.12. It may help to convince the reader that Littlewood ... Inequality 2.12 says that if the εI's all have small absolute values, then the ...
... case.) Now, take g e L" and let X > 0. The set {x : Mg(g)(a) > X} consists ... inequality for the Hardy–Littlewood maximal function. Now take fe LP, with 1 ... inequality implies that 2 ( M.G.)0) = x2's 16 2 An Elementary Introduction.
... case of p = oo is trivial. The kind of argument used to prove Theorem 2.2 is ... case of the Marcinkiewicz Interpolation Theorem. The “fine structure” of Ma ... Inequality 2.15 says that, if we restrict our attention to an interval, then ...
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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 |