## 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 54

We might want to work in L4,

**with**its norm defined by f4≡ (∫ |f(x)|4dx ) 1/4. To make things specific, ... also has the property that, if 1 <p< ∞, and f ∈

**Lp**, the

**Lp**norms of S(f) and f are comparable. The combination of these two ...

We have also tried to avoid excessive overlap

**with**other books on weighted norm inequalities. ... We prove the bounded- ness of the Hardy-Littlewood operator on

**Lp**(

**w**) for

**w**∈ Ap and we prove an extrapolation result—because we need ...

In this section I will try to acquaint the reader

**with**what things are taken for granted in weighted ... Roughly speaking, this includes: the theory of the Lebesgue integral (in 1 and d dimensions),

**Lp**spaces in Rd (1 ≤ p ≤ ∞) and ...

Sticking

**with**Our example, suppose there are two positive, finite constants, C1 and C2, such that, ... if Q is any cube

**with**((Q) > R, then 1 - f|da: • 1.4 This hypothesis is not very restrictive: it is satisfied by every fe

**LP**, ...

If we sum up 2.6 over all dyadic I

**with**length 2" and all dyadic J.

**with**length 2", we get XL fiX1(a) – XL f/XJ (a) ... Here is a question: To what extent does this equivalence extend to other L” spaces, and even to weighted

**LP**spaces?

### 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 |