## 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 38

...

**Rd**—say, x = (x 1, x2, ... , xd)—then we define x's norm, x, to be ( ∑ d1x2n)1/2. This norm has the good property that, if y = (y1, y2, ..., yd) is any other vector in

**Rd**, and |yn |≤|x n | for each n, then y ≤ x. In other words, the ...

Michael Wilson. has the same domination property possessed by the Euclidean norm on

**Rd**: if g = ∑ γnφn and |γn |≤|λ n | for all n, then g2 ≤ f2. Even better, if, for some ε > 0, we have |γn | ≤ε|λn | for all n, then g2 ≤ εf2 ...

...

**Rd**f(x)e−2πix·ξ dx, originally defined for f∈ L1(

**Rd**), and then by extension to f∈ L2. We have the Fourier inversion formula f(x) = ∫

**Rd**ˆf(ξ)e2πix·ξ dξ, which holds pointwise for appropriate f, and extends, by beginning functional ...

...

**Rd**f(x−y)g(y)dy= ∫

**Rd**f(y)g(x−y)dy defined for appropriate pairs of functions f and g. We use C∞ 0 (

**Rd**) to denote the family of infinitely differentiable functions with compact supports. The Schwartz class S(

**Rd**) is the family of ...

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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 |