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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... functions f and g. We use C∞ 0 (Rd) to denote the family of infinitely ... function f is said to be locally integrable if ∫ K |f|dx < ∞ for every ... maximal element (in the sense of set inclusion) of F that 2 1 Some Assumptions.
... maximal element must exist because of 1.1. The collection of all such Q's is ... function, or some combination of these. Suppose it's a variable t. We ... functions f(t) and g(t), and want to show f(0) = g(0). This is an immediate ...
... function of t(log(e.-- t))"—and the reader should check this one, too. Unless we are very interested in the values ... maximal Q'e F.A. (This, by the way, holds even if FA is empty: check the logic!) Call this family of maximal cubes F ...
Michael Wilson. The function g is good because it is bounded. It is bad because it might have unbounded support. The function ... maximal dyadic cubes satisfying #/ - f| da = \. K.I./." By Our Observation, 1 #/. |f|da s 2"X for every Qe FA ...
... maximal function of f, Md(f), is defined by: Md(f)(x)≡ supI:x∈I∈D|f|I. We will be seeing a lot of maximal functions like these. Before actually proving Theorem 2.1, we will make a rather long digression to investigate some of their ...
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 |