## 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 86

...

**f**Even 2 . norm on 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**...

...

**f**( y ) g ( x − y ) dy defined for appropriate pairs of

**functions**ƒ and g . We use Co ( Rd ) to denote the family ...

**let**( I ) denote I's length ( which is the same as I ) . A cube QC Rd is a cartesian product of d intervals all ...

...

**let F**、 be the family of dyadic cubes Q such that 1 dx > X. Our hypothesis on ƒ implies that every Q € F 、 is contained in some maximal Q ' F. ( This , by the way , holds even if F 、 is empty : check the logic ! ) Call this family ...

... f into finitely many pieces , N f = Σfi , 1 and showing that each T ( fi ) is “ well - behaved ” in some fashion ...

**Let f**satisfy 1.4 . For every λ > 0 , there is a ( possibly empty ) family F of pairwise disjoint dyadic cubes ...

...

**Let**D be the collection of dyadic intervals on R. For every I Є D , we

**let**It and I , denote ( respectively ) the ... (

**f**) = √

**f**( x ) h ( 1 ) ( x ) dx = = {

**f**, h ( 1 ) , where we are using ( . , . ) to An Elementary Introduction.

### 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 |