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Some estimates on these spaces for the classical operators in harmonic analysis, such as the Hardy--Littlewood maximal operator, the Calder\\'on--Zygmund operator, the Riesz potential, singular integral operators with the rough kernel, the Marcinkiewicz integral, the Bochner-Riesz operator, the Littlewood-Paley $g$ function and the intrinsic square function, are considered. Our main method is extrapolation. 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