## 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 48

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**exercises**at the end of almost every 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 ...

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**exercise**is to generalize the second

**exercise**to Rd. The first

**exercise**has this consequence: If F ⊂ Dd is any collection of dyadic cubes such that sup Q∈F l(Q) < ∞ (1.1) then there exists a disjoint collection F ⊂ F such that every ...

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**exercise**for the reader. Equation 2.4 implies that, for all dyadic intervals I, X if I is a subset of some Jk: AI (f) = { I(f1) k (2.5) Al (f2) otherwise. To put all this in plain, but approximate, language: AI (f) measures f's ...

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**exercises**at the end of the next 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 ...

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**exercises**. The splitting argument we used to prove Theorem 2.2 implies that, for every X > 1, |{a e I : Mg(f)(a) > X}| < # / |f(t) dt, (2.17) - |f|>X/2 with the bound of |{a e I : Mg(f)(a) > X}| < 1 (2.18) for X s. 1. If we multiply ...

### 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 |