A remark to the L2 boundedness of parametric Marcinkiewicz integral

Recently, A. Al-Salman (2011) [1] gave a characterization of the L2 boundedness of the parametric Marcinkiewicz integral when ρ is a positive real number. In this note, using a quite elementary method, we give a sufficient and necessary condition for the L2(Rn) boundedness of when ρ is a complex number.