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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... t have to be. The square function S(f)(x) is defined as a weighted sum (or integral) of the squares of the inner products, |〈f,φ〉| 2 , where φ belongs to the fixed collection. The function S(f)(x) varies from point to point, but, if f ...
... T(f), is bounded pointwise by a function T, S(f), ̃ S(T(f)), where the S(·) ̃ square function is an operator ... by T, S(f), ̃ because which one is can controlled say: |T(f)| by is controlled by |f|. Obviously, the closer the ...
... t talk about wavelets. The expert will see the close connections between wavelets and the material in chapters 5–7. The non-expert doesn't have to worry about them to understand the material; but, should he ever encounter wavelets, a ...
... 5 and 6 in [ 21 ] . Roughly speaking , this includes : the theory of the 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 ...
... t under consideration, A(t) ≤ CB(t). (1.2) We often want to prove such inequalities because they help us prove equations. For example, we might have two complicated but continuous functions f(t) and g(t), and want to show f(0) = g(0) ...
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 |