## 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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... theorem dumped onto his lap. The portmanteau theorem (Theorem 7.1) does come; but we trust that, when it does, the ...

**proof of Theorem**3.8 from chapter 3. This ingenious argument, due to Fedor Nazarov, completely avoids the use of ...

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**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 ...

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**proof**. 2 An Elementary Introduction We begin with the simplest object. The reader could reasonably ask what purpose ... (

**Theorem**1.1 ) first appears in [ 8 ] . The treatment here is based on that in [ 53 ] . To put all this in plain ...

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**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 ...

Michael Wilson. The

**proof of Theorem**2.2 is based on the following well - known equation : For any 0 < p < ∞ , Lx | f ( x ) dμ = p = P f x2 - 1μ ( { x : | f ( x ) | > \ } ) d \ , ( 2.14 ) which is valid for any measure space ( X , M , μ ) ...

### Cuprins

1 | |

9 | |

Exponential Square 39 | 40 |

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 GoodX | 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 |