Weighted Estimates For A Class Of Commutator Of Fractional Integral Operators In Non-doubling Measures Spaces

In this paper, we mainly study the weighted boundness of the commutators of fractional integrals operators with non-doubling measures, and the weak-type esti-mates for multilinear fractional integral commutators in non-homogeneous spaces. The whole paper is divided into three chapters.In the first chapter, we are mainly devoted to the concepts of the fractional integrals commutators and the multilinear fractional integrals commutators,and overview the celebrated results and relative conclusions.And briefly introduced the non-doubling spaces,correspondingly there are similar results of the commutators of fractional integral operates and the multilinear fractional integral commutators in non-doubling measure spaces.In the second chapter, we study the cummutator generated by the fractional integrals operator and a function in RBMO. In virtue of the estimation of the sharp maximal function, we obtain that the commutator is weighted bounded from Lp(Rd) to Lp(Rd) in non-doubling measure spaces.In the third chapter, in non-homogeneous spaces by means of the estimation of the fractional sharp maximal function, we discuss the weak-type estimates of the commutator generated by a class of multilinear fractional integral operators and a function in RBMO(μ).