Commutators Of Marcinkiewicz Integral Number Of Issues

In this paper we mainly study the boundedness of the commutator generated by smooth functions and Marcinkiewicz integral, and the weighted estimates for the Marcinkiewicz multilinear commutators, in which the kernels of Marcinkiewicz integrals satisfy bounded condition or a class of Dini condition.In chapter 1, we introduce the conception, significance and development of Marcinkiewicz integral. In chapter 2, we proved the commutator generated by Marcinkiewicz integralμΩand Besov functions b was bounded from Ld to Lr and from Ld to Fdβ-1/(np),∞. In chapter 3, we discussed the weighted (p,p) bounded-ness and the weighted weak L log L type estimates for the multilinear commutator generated by Orlicz functions and Marcinkiewicz integralμΩwith bounded kernel In chapter 4, we studyed the weighted (p, q) boundedness and the weighted weak L(log L)m type estimates for the multilinear commutator generated by BMO func-tions and Marcinkiewicz integral fin with a class of Dini kernel.