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