## 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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Michael Wilson. Weighted

**Littlewood**-

**Paley Theory**and Exponential-Square Integrability 2) Springer Lecture Notes in Mathematics 1924 Editors: J.-M. Morel, Cachan F. Michael Wilson Front Cover.

Michael Wilson. Lecture Notes in Mathematics 1924 Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris Michael Wilson Weighted

**Littlewood**-

**Paley Theory**and Exponential-Square Integrability BC Author.

Michael Wilson. Michael Wilson Weighted

**Littlewood**-

**Paley Theory**and Exponential-Square Integrability BC Author Michael Wilson Department of Mathematics University of Vermont Burlington,

Michael Wilson. I dedicate this book to my parents, James and Joyce Wilson. Preface

**Littlewood**-

**Paley theory**can be thought of as a profound.

Michael Wilson. Preface.

**Littlewood**-

**Paley theory**can be thought of as a profound generalization of the Pythagorean theorem. If x ∈ Rd—say, x = (x 1, x2, ... , xd)—then we define x's norm, x, to be ( ∑ d1x2n)1/2. This norm has the good ...

### 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 |