The Boundedness Of Commutator Of Fractional Integral Operator And Marcinkiewicz Integrals

In this paper, the first chapter discusses the boundedness of and the commutator T_Ω,μ^{b ,m}, generated by Lipschitz function b and the fractional integral operatorT_Ω,μ, on the Hardy-type space H_b^m,s^b,m(Rⁿ)and Herz-type Hardy Space H_b^mK_q^a,p(Rⁿ). The seconder chapter presents the properties of the commutatorμ_Ω^b generalized by the Marcinkiewiacz integralμ_Ωwith homogeneous kernel and some weighted Lipschitz functionb . By using the properties of the sharp maximal function, the L^P (v),L^q ( v^1-q)-boundedness of the operatorμ_Ω^b is established.