# Weighted Littlewood-Paley Theory and Exponential-Square Integrability

Part of the Lecture Notes in Mathematics book series (LNM, volume 1924)

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Part of the Lecture Notes in Mathematics book series (LNM, volume 1924)

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.

Singular integral Square function exponential-square maximal function weighted inequality

- DOI https://doi.org/10.1007/978-3-540-74587-7
- Copyright Information Springer-Verlag Berlin Heidelberg 2008
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-540-74582-2
- Online ISBN 978-3-540-74587-7
- Series Print ISSN 0075-8434
- Buy this book on publisher's site