## 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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**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 little about the Fourier transform . We will use certain definitions ...

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**Lebesgue**measure by | E | . We will try to make it clear from the context when │ · | means the measure of a set and when it means the absolute value of a number . We will also use | · | to denote the norm of a vector in Rd . If I CR is ...

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**Lebesgue**differentiation theorem , [ ƒ | ≤ \ almost every- where off the set UFQ . Now , what is this good for ? Harmonic analysis is about the action of linear operators on functions . Usually we are trying to show that some operator ...

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**Lebesgue**differentiation theorem implies that ƒ is a.e. constant on ( 0 , ∞ ) . Obviously , the same argument works as well on ( -∞ , 0 ) . This proves completeness . Elementary functional analysis now implies that , for all ƒ € L2 ...

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**Lebesgue**one . For example , it turns out that , if 1 < p < ∞ , there are constants cp and Cp so that , for all fe LP ( R ) , Cp || f || p ≤ || S ( ƒ ) || p ≤ Cp || f || p This fact is so central to what we will be doing that it ...

### 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 |