## 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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**Haar**coefficient for the interval I. By Bessel's Inequality, we immediately have: |AI(f) < || |f(x) dr »n's/ for any ...

**sum**XE, A1(f)h(r) converges to f in L*, and that //øfør-XIMU)". (2.2) I We will be saying a lot about 2.2, but ...

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**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 this argument. We are allowed to say the following: If ...

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

... sum to be a lot bigger than a sum of squares, but inequality 2.10 says that, on the average, this isn't true for

**sums of Haar**functions. The reason is that the sum ∑ I λI(f)h(I) has a lot of cancelation in it. It's remarkable that this ...

...

**Haar**functions aren't wavelets, strictly speaking, but they're near enough for this example. Suppose we have a function f which belongs to some Lp(R), with 1 < p < ∞. It is fundamentally important to know to what extent the

**sum**∑ I λI ...

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### 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 |