## 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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... we need both—but we don't prove Ap factorization or the Rubio de Francia extrapolation theorem, excellent treatments of which can be found in many books (e.g., [16] and [24]). The book is laid out this way.

**Chapter**1 covers Preface IX.

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**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 a ...

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**chapter**. Some of them expand on topics treated in the text; some tie up loose ends in proofs; some are referred to later in the book. We encourage the reader to understand all of them and to attempt at least a few. (We have supplied ...

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**chapters**5 and 6 in [21]. Roughly speaking, this includes: the theory of the Lebesgue integral (in 1 and d dimensions), Lp spaces in Rd (1 ≤ p ≤ ∞) and their duals, and some functional analysis. We also assume that the reader knows a ...

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**chapter**. We feel it fair to warn the reader that this “simpler” proof has complications of its own, including discussions of things which, at first, seem to have nothing to do with the square function. Our proof of Theorem 2.1 will not ...

### 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 |