## 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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Rezultatele 1 - 5 din 32

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**norm**, || x || , to be ( x2 ) 1/2 . This

**norm**has the good property that , if y = ( y1 , Y2 , ... , ya ) is any other vector in Rd , and | yn | xn | for each n , then || y || || x || . In other words , the size of x , as measured by ...

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**norm**on Rd: better, if, for Unfortunately, L2 is not always the most useful function space for a given problem. We might want to work in L4, with its

**norm**defined by 1/4 f 4 ≡ (∫ |f(x)| ) 4 dx . To make things specific, let's suppose ...

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**norm**inequalities) imply that this connection is pretty close. We have tried to make this book self-contained, not too long, and ac- cessible to non-experts. We have also tried to avoid excessive overlap with other books on weighted

**norm**...

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**norm**inequalities. 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 ...

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**norm**means different things for different p . For small p , it means that ƒ has good decay at infinity ; for large p , it tells us that ƒ doesn't ever " spike " too sharply . So , an inequality like 2.12 says that ( f ) h ( 1 ) can ...

### 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 |