Weighted Littlewood-Paley Theory and Exponential-Square Integrability

2008
ISBN: 978-3-540-74582-2
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1924, 227 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 376 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Wilson, Michael

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Some Assumptions.- An Elementary Introduction.- Exponential Square.- Many Dimensions; Smoothing.- The Calderón Reproducing Formula I.- The Calderón Reproducing Formula II.- The Calderón Reproducing Formula III.- Schrödinger Operators.- Some Singular Integrals.- Orlicz Spaces.- Goodbye to Good-?.- A Fourier Multiplier Theorem.- Vector-Valued Inequalities.- Random Pointwise Errors.

Über Autor(innen)

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.