Weighted Littlewood-Paley Theory and Exponential-Square Integrability, Ediția 1924

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Springer Science & Business Media, 2008 - 224 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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Cuprins

Some Assumptions
1
An Elementary Introduction
9
Exponential Square
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
144
Orlicz Spaces
161
Goodbye to Goodλ
189
A Fourier Multiplier Theorem
197
VectorValued Inequalities
203
Random Pointwise Errors
213
References
219
Index
222
Drept de autor

Some Singular Integrals
151

Alte ediții - Afișați-le pe toate

Termeni și expresii frecvente

Pasaje populare

Pagina 221 - Weighted norm inequalities for the continuous square function," Trans. Amer. Math. Soc. 314 (1989), 661-692. [W3] — , "Some two-parameter square function inequalities," to appear in Indiana University Math.
Pagina 221 - EM STEIN, On some functions of Littlewood-Paley and Zygmund, Bull. Amer. Math. Soc. 67 (1961), 99-101.

Despre autor (2008)

Michael Wilson received his PhD in mathematics from UCLA in 1981. After post-docs at the University of Chicago and the University of Wisconsin (Madison), he came to the University of Vermont, where he has been since 1986. He has held visiting positions at Rutgers University (New Brunswick) and the Universidad de Sevilla.

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