Boundedness of Marcinkiewicz integrals and their commutators in H 1 (ℝ n × ℝ m )

Abstract

The authors establish the boundedness of Marcinkiewicz integrals from the Hardy space H 1 (ℝ n × ℝ m ) to the Lebesgue space L 1(ℝ n × ℝ m ) and their commutators with Lipschitz functions from the Hardy space H 1 (ℝ n × ℝ m ) to the Lebesgue space L q (ℝ n × ℝ m ) for some q > 1.