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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... dyadic square function. Chapters 5, 6, and 7 are devoted to the Calderón reproducing formula. The Calderón formula provides a canonical way of expressing “arbitrary” functions as linear sums of special, smooth, compactly supported functions ...
... function f is said to be locally integrable if ∫ K |f|dx < ∞ for every compact subset of f's domain. This domain ... dyadic interval is one of the form [j/2k,(j + 1)/2k), where j and k are integers. A dyadic cube Q ⊂ Rd is a cube ...
... function of t(log(e.-- t))"—and the reader should check this one, too ... dyadic cubes Q such that 1 - d X. :// QC = Our hypothesis on f implies that ... dyadic cube such that Q C Q and (Q) = 26(Q). Then, because of Q's maximality ...
... functions, due to A. P. Calderón and A. Zygmund, is based on the foregoing observation about dyadic cubes. It lets us write any function f satisfying 1.4 as the sum of two functions (usually called g and b, for “good” and “bad”). As we ...
Michael Wilson. The function g is good because it is bounded. It is bad because it might have unbounded support. The function ... dyadic cubes satisfying #/ - f| da = \. K.I./." By Our Observation, 1 #/. |f|da s 2"X for every Qe FA. Define - ...
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 |