The Boundedness Of Commutators Of Marcinkiewicz Integral With Varible Kernels

In this paper, we mainly study the boundedness of the commutator μ_Ω,b(f) which is formed by the Marcinkiewicz integral operator with variable kernels and a function b∈(∧|·)_β(R_n).This paper is composed of two chapters.In the first chapter, we briefly recall the histories of the operator which we study in this article. We also have an introduction to variable kernels. And at last we list our main results.In the second chapter, we discuss and get the boundedness of μ_Ω,b(f) from L^p to L^q(1 < p < ∞), the weak type L¹ boundedness and the boundedness from H^p to L^q(n/(n+β)