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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Pagina 4
... functions is A(t)=t(log(e+t)) and B(t)=t(log(534-H t”)), where the range of admissible t's is [0, oo); the reader ... f is a locally integrable function with the property that, for every e > 0, there exists an R = 0 such that, if Q is ...
... functions is A(t)=t(log(e+t)) and B(t)=t(log(534-H t”)), where the range of admissible t's is [0, oo); the reader ... f is a locally integrable function with the property that, for every e > 0, there exists an R = 0 such that, if Q is ...
Pagina 5
... F can be chosen so that ∑ F|Q|≤ 2λ ∫ |f|>λ/2|f|dx. (1.5) and ∫ Before proving the theorem, we should explain how the functions g and b are good and bad in their own ways. The function g is good because it is bounded. It 1 Some ...
... F can be chosen so that ∑ F|Q|≤ 2λ ∫ |f|>λ/2|f|dx. (1.5) and ∫ Before proving the theorem, we should explain how the functions g and b are good and bad in their own ways. The function g is good because it is bounded. It 1 Some ...
Pagina 7
... f – fl. Notice that |fo| < \/2 everywhere. Now we apply the previous splitting argument to fi, but use A/2 as our cut-off height, instead of A. We obtain two functions ... functions bø satisfy the support and cancelation conditions, and also ...
... f – fl. Notice that |fo| < \/2 everywhere. Now we apply the previous splitting argument to fi, but use A/2 as our cut-off height, instead of A. We obtain two functions ... functions bø satisfy the support and cancelation conditions, and also ...
Pagina 10
... (f) is known as f's Haar coefficient for the interval I. By Bessel's Inequality, we immediately have: |AI(f) < || |f(x) dr »n's/ for any fe L*(R). We claim that the Haar functions actually form a complete orthonormal system for L*(R). To ...
... (f) is known as f's Haar coefficient for the interval I. By Bessel's Inequality, we immediately have: |AI(f) < || |f(x) dr »n's/ for any fe L*(R). We claim that the Haar functions actually form a complete orthonormal system for L*(R). To ...
Pagina 12
... (f)h(n)(c), 1. We can rewrite the last sum as XL XI (f)h(1)(a). Ie D: IOC I 6(IO).<e (I) <2\ e(Io) There is clearly nothing special about 10, IN, Or a in ... function, via Haar functions, to get information 12 2 An Elementary Introduction.
... (f)h(n)(c), 1. We can rewrite the last sum as XL XI (f)h(1)(a). Ie D: IOC I 6(IO).<e (I) <2\ e(Io) There is clearly nothing special about 10, IN, Or a in ... function, via Haar functions, to get information 12 2 An Elementary Introduction.
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 |
Termeni și expresii frecvente
absolutely convergent adapted functions argument assume belong bounded by(t Calderón formula Calderón reproducing formula Cauchy–Schwarz inequality chapter Chebyshev's inequality compact support compact-measurable exhaustion Corollary cubes Q define definition denote depending disjoint dt dy dyadic cubes dyadic doubling dyadic square function equation estimate everywhere exercise fe LP finishes the proof finite linear sums functions f Haar functions Hölder inequality holds implies Lebesgue Lebesgue measure Let f Let Q Littlewood-Paley theory locally integrable log(e–H LP norm LP spaces LP(w Ma(f Ma(v Martina Franca maximal function maximal operator measurable function measure space Moar non-negative Orlicz maximal Orlicz norms Orlicz space pointwise positive constant positive numbers Proof of Theorem Rademacher function radial Rd Rd reader result satisfies sequence subset sums of adapted sums of Haar support contained Suppose supremum Theorem 2.1 Tk(f yields Young function
Informații bibliografice
| Titlu | Weighted Littlewood-Paley Theory and Exponential-Square Integrability Lecture Notes in Mathematics |
| Autor | Michael Wilson |
| Ediție | ilustrată |
| Editor | Springer, 2007 |
| ISBN | 3540745874, 9783540745877 |
| Lungime | 227 pagini |
| Exportă citatul | BiBTeX EndNote RefMan |