Weighted Littlewood-Paley Theory and Exponential-Square IntegrabilityLittlewood-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. |
Din interiorul cărții
Pagina ix
The exponential-square results (and the corresponding weighted norm inequalities) imply that this connection is pretty ... result—because we need both—but we don't prove Ap factorization or the Rubio de Francia extrapolation theorem, ...
The exponential-square results (and the corresponding weighted norm inequalities) imply that this connection is pretty ... result—because we need both—but we don't prove Ap factorization or the Rubio de Francia extrapolation theorem, ...
Pagina x
In chapter 4 we extend the results of the preceding chapters to d dimensions and to continuous analogues of the dyadic square function. Chapters 5, 6, and 7 are devoted to the Calderón reproducing formula. The Calderón formula provides ...
In chapter 4 we extend the results of the preceding chapters to d dimensions and to continuous analogues of the dyadic square function. Chapters 5, 6, and 7 are devoted to the Calderón reproducing formula. The Calderón formula provides ...
Pagina 1
Every area of mathematics—and, indeed, of learning—is a minefield of presuppositions and “well-known” results. In this section I will try to acquaint the reader with what things are taken for granted in weighted LittlewoodPaley theory.
Every area of mathematics—and, indeed, of learning—is a minefield of presuppositions and “well-known” results. In this section I will try to acquaint the reader with what things are taken for granted in weighted LittlewoodPaley theory.
Pagina 13
(2.8) We have approached this formula through an L2 result 2.2, which says that f2 = S(f)2 (2.9) for f ∈ L2. Before going one step further, it will be profitable to reflect on the meaning of 2.9. It is a peculiar equation.
(2.8) We have approached this formula through an L2 result 2.2, which says that f2 = S(f)2 (2.9) for f ∈ L2. Before going one step further, it will be profitable to reflect on the meaning of 2.9. It is a peculiar equation.
Pagina 17
However, if f's support is contained in a dyadic interval I, we have two substitute results. The first OIle IS //ølo" fol/l)" /M (nar (2.1% I I The second result is # | (Ma(f))” dr & Co (# | |f| *). (2.16) valid for 0 < 3 < 1.
However, if f's support is contained in a dyadic interval I, we have two substitute results. The first OIle IS //ølo" fol/l)" /M (nar (2.1% I I The second result is # | (Ma(f))” dr & Co (# | |f| *). (2.16) valid for 0 < 3 < 1.
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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,Professor 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 |