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Weighted inequalities for the dyadic square function. (English) Zbl 1362.42049

Summary: We study Fefferman-Stein inequalities for the dyadic square function associated with an integrable, Hilbert-space-valued function on the interval \([0, 1)\). The proof rests on a Bellman function method: the estimates are deduced from the existence of certain special functions enjoying appropriate majorization and concavity.

MSC:

42B25 Maximal functions, Littlewood-Paley theory
60G44 Martingales with continuous parameter
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