## Weighted Littlewood-Paley Theory and Exponential-Square IntegrabilityLittlewood-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 21

We assume that the reader has had a graduate course in

**measure**theory, at least to the level of chapters 5 and 6 in [21]. Roughly speaking, this includes: the theory of the Lebesgue integral (in 1 and d dimensions), Lp

**spaces**in Rd (1 ...

A

**measurable**function f is said to be locally integrable if ∫ K |f|dx < ∞ for every compact subset of f's domain. This domain will always be Rd or some nice subset of it (such as an interval, ball, rectangle, or half-

**space**).

general fact about Hilbert

**spaces**, and so hides the numerical nitty-gritty in this special case. ... These include Lp (p = 2) and so-called weighted

**spaces**, in which the underlying

**measure**is no longer the familiar Lebesgue one.

The proof of Theorem 2.2 is based on the following well-known equation: For any 0 < p < oo, / |f(x)" du = p / who fool-Apax (210 X O which is valid for any

**measure space**(X, M, pl). (Equation 2.14 is frequently stated to hold for ...

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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 - Afișați-le pe toate

Weighted Littlewood-Paley Theory and Exponential-Square ..., Ediția 1924 Michael Wilson,Professor Michael Wilson Previzualizare limitată - 2008 |