Littlewood–Paley–Stein Theory with Respect to the Gaussian Measure

Littlewood–Paley–Stein theory is an important area in harmonic analysis, with a great number of applications, as Littlewood–Paley functions are very useful in the proof of the Lp boundedness of singular integral operators, and in the characterization of Hardy spaces. E. Stein, in his beautiful monograph [253] showed how the classical notions of the Littlewood–Paley theory could be extended well beyond the Euclidean setting and also showed explicitly its link to the martingale theory in probability.