## 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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...

**1**/2 . This norm has the good property that , if y = ( y1 , Y2 , ... , ya ) is any other vector in

**Rd**, and | yn | xn | for each n , then || y || || x || . In other words , the size of x , as measured by the norm function , is determined ...

...

**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 suppose that our ...

... 1 and d dimensions ) , LP spaces in

**Rd**(

**1**≤ p ≤ ∞ ) and their duals , and some functional analysis . We also assume that the reader knows a little about the Fourier transform . We will use certain definitions and conventions ...

... (

**1**+ [ x ] ) dx < ∞0 . A measurable function ƒ is said to be locally integrable if Sk | 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 ...

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### 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 |