Weighted Littlewood-Paley theory and exponential-square integrability / Michael Wilson

Littlewood-Paley theory is an essential tool of Fourier analysis. The present book tries to give a gentle, well-motivated introduction to this theory for graduate students. Chapter 1 covers some elementary facts about dyadic cubes and the Calderón-Zygmund decomposition. Chapters 2, 3 and 4 discuss Littlewood-Paley theory including weighted estimates. Chapters 5,6 and 7 are devoted to the Calderón’s reproducing formula. The latter half of this book gives some applications: Applications of weighted Littlewood-Paley theory to the analysis of Schrödinger and singular integral operators, Littlewood-Paley theory on Orlicz spaces, a new proof of the Hörmander-Mihlin multiplier theorem and so on. Exercises are put at the end of almost every chapter. The author emphasizes that one needs to consider weighted estimates to investigate the connection between a function and its square function. ... (Zentralblatt)