## 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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**Rd**, and | yn | xn | for each n , then || y || || x || . In other words , the size of x , as measured by the norm function , is determined entirely by the sizes of x's components . This remains true if we let the dimension d increase to ...

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**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 that our ...

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**Rd**originally defined for ƒ € L1 (

**Rd**) , and then by extension to ƒ € L2 . We have the Fourier inversion formula f ( x ) =

**Rd**Lay F ( 6 ) e2xix . & dɛ . which holds pointwise for appropriate ƒ , and extends , by beginning functional ...

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**Rd**or some nice subset of it ( such as an interval , ball , rectangle , or half - space ) . The only half - space we ever look at is

**Rd**+ 1 , which equals Rdx ( 0 , ∞ ) . We denote the space of locally integrable functions defined on

**Rd**...

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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 |