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LMS: 114 Lectures on Bochner Riesz (London Mathematical Society Lecture Note Series)

LMS: 114 Lectures on Bochner Riesz (London Mathematical Society Lecture Note Series)

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Katherine Michelle Davis
Cambridge University Press, 8/21/2008
EAN 9780521312776, ISBN10: 0521312779

Paperback, 160 pages, 22.9 x 15.2 x 1 cm
Language: English

This book is concerned with the modern theory of Fourier series. Treating developments since Zygmund's classic study, the authors begin with a thorough discussion of the classical one-dimensional theory from a modern perspective. The text then takes up the developments of the 1970s, beginning with Fefferman's famous disc counterexample. The culminating chapter presents Cordoba's geometric theory of Kayeka maximal functions and multipliers. Research workers in the fields of Fourier analysis and harmonic analysis will find this a valuable account of these developments. Second year graduate students, who are familiar with Lebesgue theory and are acquainted with distributions, will be able to use this as a textbook which will bring them up to the exciting open questions in the field.

Introduction
Preliminaries
1. Multiplier theory
2. The Hilbert transform
3. Good lambda and weighted norm inequalities
4. Multipliers with singularities
5. Singularities along curves
6. Restriction theorems
7. The multiplier theorem for the disc
8. The Cordoba multiplier theorem
References
Index.