Lecture Notes in Mathematics

By: Michael Wilson

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Paperback | 18 October 2007

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244 Pages

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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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From the reviews: "This engaging book by J. Michael Wilson concentrates on weighted inequalities of the forms ! . The subject matter is presented in a fashion accessible to an advanced graduate student. Proofs of major ! results are usually given in full. ! There are a good number of exercises at the end of each chapter ! . In addition there are many suggestions in the body of the text to prove or further investigate a given result." (Caroline P. Sweezy, Mathematical Reviews, Issue 2008 m)

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Probability & Statistics Functional Analysis & Transforms

Some Assumptions	p. 1
An Elementary Introduction	p. 9
Exponential Square	p. 39
Many Dimensions; Smoothing	p. 69
The Calderon Reproducing Formula I	p. 85
The Calderon Reproducing Formula II	p. 101
The Calderon Reproducing Formula III	p. 129
Schrodinger Operators	p. 145
Some Singular Integrals	p. 151
Orlicz Spaces	p. 161
Goodbye to Good-[lambda]	p. 189
A Fourier Multiplier Theorem	p. 197
Vector-Valued Inequalities	p. 203
Random Pointwise Errors	p. 213
References	p. 219
Index	p. 223
Table of Contents provided by Ingram. All Rights Reserved.

Lecture Notes in Mathematics

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