## 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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**estimates**similar to—S(·). This makes it possible to understand the S(T(f)), which is behavior controlled of by T, S(f), ̃ because which one is can controlled say: |T(f)| by is controlled by |f|. Obviously, the closer the connection ...

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**estimate**directly, but B(t) is easy (or easier) to handle. An inequality like 1.2 usually follows from a chain of inequalities, like so, A(t) ≤ C1A1 (t) ≤ C2A2 (t) ≤ ··· ≤ C129 B(t), but usually not so long. However, unless one is ...

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**estimates**of Cp and Cp tell us how careful we have to be in computing the λ ( ƒ ) ' s , if we want this representation to be faithful . Our first major goal is a proof of Theorem 2.1 . There are at least two approaches we could take ...

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**estimate**for { x : Ma ( f ) ( x ) > \ } ] and apply 2.14 : [ ( Md ( f ) ) " dx ≤ p f 2 \ p - 1 \ √ √ { t : \ f ( t ) \ > \ / 2 } ' [ 18 | f ( t ) | dt | dx = = 2o ( 2P ( Р Ρ Р - Р - r2 | f ( t ) | 2pXP - 2 dx dt [ \ f ( t ) || f ( t ) ...

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**estimates**by p \ o - 1 ( i.e. , 1 ) and integrate from 0 to ∞ , we get [ Ma ( f ) dx ≤ [ * \ { x € 1 : Ma ( f ) ( x ) > \ } | d \ J + م • ∞ C 入\ f \ > \ / 2 | f ( t ) | dt | dx r2 | f ( t ) | < 1 + C < 1+ √ \ f ( t ) | log * ( \ f ( t ) ...

### 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 |