## 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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**holds**for all f in suitable test classes, for various ranges of p (usually, 1 <p< ∞). He will also learn some necessary conditions for such inequalities. The usefulness of the square function (in its many guises) comes chiefly from the ...

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**holds**pointwise for appropriate ƒ , and extends , by beginning functional analysis , to all ƒ L2 . Our definition of the Fourier transform satisfies and || ƒ || 2 = || ƒ || 2 ( ƒ * g ) ( E ) = ƒ ( E ) ĝ ( E ) , where f g is the usual ...

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**holds**even if F 、 is empty : check the logic ! ) Call this family of maximal cubes F. If QEF , then 1 1Q1 // flde > > λ . I claim that , as well , 1 12 / \ f \ dex < 2d ) . To see this , let Q be the unique dyadic cube such that Q C Q ...

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**hold**for σ - finite measure spaces , and proved by Fubini - Tonelli . If the reader tries to do this , he will find that the trickiest step comes in proving the measurability of certain sets in X × ( 0 , ∞ ) . If he's lucky , he'll ...

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### 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 |