## 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 6 - 10 din 91

...

**functions**is A(t)=t(log(e+t)) and B(t)=t(log(534-H t”)), where the range

**of**admissible t's is [0, oo); the reader ...

**f**is a locally integrable

**function**with the property that, for every e > 0, there exists an R = 0 such that, if Q is ...

...

**F**can be chosen so that ∑

**F**|Q|≤ 2λ ∫ |

**f**|>λ/2|

**f**|dx. (1.5) and ∫ Before proving the theorem, we should explain how the

**functions**g and b are good and bad in their own ways. The

**function**g is good because it is bounded. It 1 Some ...

...

**f**– fl. Notice that |fo| < \/2 everywhere. Now we apply the previous splitting argument to fi, but use A/2 as our cut-off height, instead

**of**A. We obtain two

**functions**...

**functions**bø satisfy the support and cancelation conditions, and also ...

... (

**f**) is known as

**f's**Haar coefficient for the interval I. By Bessel's Inequality, we immediately have: |AI(

**f**) < || |

**f**(x) dr »n's/ for any fe L*(R). We claim that the Haar

**functions**actually form a complete orthonormal system for L*(R). To ...

... (

**f**)h(n)(c), 1. We can rewrite the last sum as XL XI (

**f**)h(1)(a). Ie D: IOC I 6(IO).<e (I) <2\ e(Io) There is clearly nothing special about 10, IN, Or a in ...

**function**, via Haar

**functions**, to get information 12 2 An Elementary Introduction.

### 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 |