We prove the L p boundedness of a class of parametric Marcinkiewicz integral operators M ,h when h satisfies a certain integrability condition and belongs to the block space B (0,-1/2) q (S n-1 ) for some q > 1, n 2. Also, we obtain the L p boundedness for a class of rough parametric Marcinkiewicz integral operators M * , ,h, and M ,h,S related to the Littlewood-Paley g * -function and the area integral S, respectively.Our results are essential improvement and extension of some previously known results.
H. M. Al-Qassem (Thu,) studied this question.