## 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. |

### Din interiorul cărții

Rezultatele 1 - 5 din 86

...

**proof of Theorem**3.8 from chapter 3. This ingenious argument, due to Fedor Nazarov, completely avoids the use of good-λ inequalities (which we introduce in chapter 2). These have been a mainstay of analysis since the early 1970s. In the ...

...

**Proof of Theorem**1.1. We will essentially prove the theorem twice. The first proof will give us g and b that almost do what we want. Then we will show how, with only a small modification, we can get the desired g and b. To begin: let FA ...

...

**proof**. The reader could reasonably ask what purpose is served by being able to split f this way for every positive A ... (

**Theorem**1.1) first appears in [8]. The treatment here is based on that in [53]. 2 An Elementary Introduction We ...

...

**proof of Theorem**2.1. There are at least two approaches we could take here. We could give a quick-and-dirty, relatively dir- ect proof. Unfortunately, this proof does not generalize to small p (0 < p ≤ 1) or to weighted settings. The other ...

Michael Wilson. The

**proof of Theorem**2.2 is based on the following well-known equation: For any 0 < p < oo, / |f(x)" du = p / who fool-Apax (210 X O which is valid for any measure space (X, M, pl). (Equation 2.14 is frequently stated to ...

### 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 |