Weighted Littlewood-Paley Theory and Exponential-Square Integrability

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Springer, 31 dec. 2007 - 227 pagini
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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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Pagini selectate

Cuprins

Some Assumptions
1
An Elementary Introduction
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
Drept de autor

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

Termeni și expresii frecvente

absolutely convergent adapted functions argument assume belong bounded by(t Calderón formula Calderón reproducing formula Cauchy–Schwarz inequality chapter Chebyshev's inequality compact support compact-measurable exhaustion Corollary cubes Q define definition denote depending disjoint dt dy dyadic cubes dyadic doubling dyadic square function equation estimate everywhere exercise fe LP finishes the proof finite linear sums functions f Haar functions Hölder inequality holds implies Lebesgue Lebesgue measure Let f Let Q Littlewood-Paley theory locally integrable log(e–H LP norm LP spaces LP(w Ma(f Ma(v Martina Franca maximal function maximal operator measurable function measure space Moar non-negative Orlicz maximal Orlicz norms Orlicz space pointwise positive constant positive numbers Proof of Theorem Rademacher function radial Rd Rd reader result satisfies sequence subset sums of adapted sums of Haar support contained Suppose supremum Theorem 2.1 Tk(f yields Young function

Despre autor (2007)

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.

Informații bibliografice

QR code for Weighted Littlewood-Paley Theory and Exponential-Square Integrability
TitluWeighted Littlewood-Paley Theory and Exponential-Square Integrability
Lecture Notes in Mathematics
AutorMichael Wilson
Edițieilustrată
EditorSpringer, 2007
ISBN3540745874, 9783540745877
Lungime227 pagini
  
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