## 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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**equations**. For example, we might have two complicated but continuous functions f(t) and g(t), and want to show f(0) = g(0). This is an immediate consequence of: |f(t) − g(t)| ≤ CB(t) limt→0 B(t)=0. In practice, |f(t) − g(t)| is hard ...

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**equation**,” A(t) • B(t). When the context does not make it clear, we will say what the admissible t's a re. We will conclude this section with a deceptively simple observation and a few of its profound consequences. Suppose that f is a ...

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**Equation**2.4 implies that, for all dyadic intervals I, X if I is a subset of some Jk: AI (f) = { I(f1) k (2.5) Al (f2) otherwise. To put all this in plain, but approximate, language: AI (f) measures f's deviation from its mean, at the ...

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**equation**S(f)(x) = ( ∑I |λI(f)|2|I|χI(x) ) 1/2 . (2.8) We have approached this formula through an L2 result 2.2, which says that f2 = S(f)2 (2.9) for f ∈ L2. Before going one step further, it will be profitable to reflect on the ...

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**Equation**2.9 says that there is a direct relation between a signal's amplitude and its energy. Later, when we consider weighted forms of 2.10, and their applications to the study of Schrödinger operators, we will make the connection ...

### 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 |