On Marcinkiewicz Integral Operators with Rough Kernels

Abstract.

This paper is devoted to the study on the L^p-mapping properties of Marcinkiewicz integral operators with rough kernels along “polynomial curves” on $\mathbb{R}^n .$ The $L^p (\mathbb{R}^n )$ boundedness of the Marcinkiewicz integrals for some fixed 1 < p < ∞ are obtained under some size conditions, which essentially improve or extend some well-known results.