## 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 43

We use C∞ 0 (Rd) to denote the family of infinitely differentiable

**functions**with compact supports. ... some Q∈ F. The proof is: For every Q∈ F, let Q be the

**maximal**element (in the sense of set inclusion) of F that 2 1 Some Assumptions.

element (in the sense of set inclusion) of F that contains Q; such a

**maximal**element must exist because of 1.1. ... We have two positive quantities—call them A and B—that depend on something else: a variable, a vector, a

**function**, ...

An example of such a pair of

**functions**is A(t)=t(log(e+t)) and B(t)=t(log(534-H t”)), where the range of admissible ... every Q € JFX is contained in some

**maximal**Q'e F.A. (This, by the way, holds even if FA is empty: check the logic!)

The

**function**g is good because it is bounded. ... The

**function**b is bad because it is in general unbounded. ... To begin: let FA (note that we have dropped the prime') be the family of

**maximal**dyadic cubes satisfying #/ - f| da = \.

The dyadic

**maximal function**of f, f∗, is given by: f∗(x) ≡ sup |fI|. I:x∈I∈D The dyadic Hardy-Littlewood

**maximal function**of f, Md(f), is defined by: Md(f)(x)≡ supI:x∈I∈D|f|I. We will be seeing a lot of

**maximal functions**like ...

### Ce spun oamenii - Scrie o recenzie

### 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,Professor Michael Wilson Previzualizare limitată - 2008 |