Weighted Estimates For Marcinkiewicz Integral Operator And Commutators

Letμbe the Marcinkiewicz integral operatorLet b be a locally integrable function on Rⁿ,定义F_t,bthen we define the Marcinkiewicz commutatorsμ_b:In this thesis, the author studies the weighted estimates for the Marcinkiewicz integral operator and commutators of Marcinkiewicz integral operators.In chapter 2, we consider the boundedness of the Marcinkiewicz integral operator with rough kernel on the weighted Herz spaces.In chapter 3, we consider the boundedness of the commutatorμ_b, with the weighted Lipschitz functions on weighted Hardy spaces, provided forμ∈A₁ and b∈BMO_ωor b∈Lip_β,ω.