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 j and b. and a disjoint family of dyadic cubes J'A such that b = XX, bø). where the functions bø satisfy the support and cancelation conditions, and also have | Wolars 2"Q/2)Q-2'No. Summing up the measures of the Q's, we get 2 ...
... dyadic Square function. Let D be the collection of dyadic intervals on R. For every I e D, we let I, and I, denote (respectively) the left and right halves of I. For each I e D, Set |I| "/* if c e II: h(1)(a) = ( – IT'/* if t e I, 0 if ...
... functions actually form a complete orthonormal system for L*(R). To see this ... dyadic interval 10 such that both a and y belong to 10. Suppose that Jo and ... function. Write f = f; + f2, where fi(a)= {{" – I' fat if a € [0, 1); 10 2 ...
... dyadic intervals, I C J, and a € I, then fi – f.J = X Ak(f)h(x)(x). (2.6) K ... dyadic I with length 2" and all dyadic J. with length 2", we get XL fiX1(a) ... function, via Haar functions, to get information 12 2 An Elementary Introduction.
... dyadic square function, which makes sense for any f∈ L1loc(R), is defined by the equation S(f)(x) = ( ∑I |λI(f)|2|I|χI(x) ) 1/2 . (2.8) We have approached this formula through an L2 result 2.2, which says that f2 = S(f)2 (2.9) for f ...
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 |