Boundedness of Littlewood Paley Operators Relative to non Isotropic Dilations

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Abstract

We consider Littlewood-Paley functions associated with a non-isotropic dilation group on ℝn. We prove that certain Littlewood-Paley functions defined by kernels with no regularity concerning smoothness are bounded on weighted Lp spaces, 1 < p < 1, with weights of the Muckenhoupt class. This, in particular, generalizes a result of N. Rivière (1971).

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