Weighted Littlewood-Paley Theory and Exponential-Square Integrability

Littlewood-Paley theory extends some of the benefits of orthogonality to situations where it doesnt make sense by letting certain oscillatory infinite series of functions be controlled in terms of infinite series of non-negative functions. Beginning in the 1980s, it was discovered that this control could be made much sharper. This book offers a gentle, well-motivated introduction to those discoveries, the methods behind them, their consequences, and some of their applications.