## 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 20

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. ... also has the property that, if 1 <p< ∞, and f ∈ Lp, the

**Lp norms**of S(f) and f are comparable.

The exponential-square results (and the corresponding weighted

**norm**inequalities) imply that this connection is pretty ... We prove the bounded- ness of the Hardy-Littlewood operator on

**Lp**(w) for w ∈ Ap and we prove an extrapolation ...

The scale of Orlicz spaces (which includes that of

**Lp**spaces for 1 ≤ p ≤ ∞) provides a flexible way of keeping track of the integrability properties of functions. It is very useful in the study of weighted

**norm**inequalities.

These include Lp (p = 2) and so-called weighted spaces, in which the underlying measure is no longer the familiar Lebesgue one. ... The reason is that having a “small”

**Lp norm**means different things for different p.

V-ați atins limita de vizualizări pentru această carte.

### Ce spun oamenii - Scrieți 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 - Afișați-le pe toate

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