The uniform quantitive weighted boundedness of fractional Marcinkiewicz integral and its commutator

Huoxiong Wu, Lin Wu

Suppose that $\hat{I}\text{c◯}\in L^{\infty }({\mathbb{S}}^{n-1})$ is homogeneous of degree zero with mean value zero. Then we consider a fractional type Marcinkiewicz integral operator $$μ_{Ω,Î…