A sparse domination for the Marcinkiewicz integral with rough kernel and applications

Xiangxing Tao, Guooen Hu

Let $\Omega$ be homogeneous of degree zero, have mean value zero and integrable on the unit sphere, and ${\mu }_{\Omega }$ be the higher-dimensional Marcinkiewicz integral defined by $$μ_Ω(f)(x)= \B…