\(L^p\) boundedness of rough Marcinkiewicz integral on product torus (Q1572929)

This paper presents a version on the product torus of the result obtained by the authors of this paper and \textit{J. Chen} [Chin. Ann. Math., Ser. A 21, No. 1, 39-44 (2000; Zbl 0960.42005)] on the boundedness of the Marcinkiewicz integral operator on a product space. In this paper, the authors prove the \(L^p({\mathbb T}^n\times {\mathbb T}^m)\)-boundedness (\(1<p<\infty\)) of the Marcinkiewicz integral operator with a rough kernel satisfying the same conditions as in the mentioned paper.