Boundedness of fractional integral operators on non-homogeneous metric measure spaces

Original · EN

In this paper, the fractional integral operator on non-homogeneous metric measure spaces is introduced, which contains the classic fractional integral operator, fractional integral with non-doubling measures and fractional integral with fractional kernel of order α and regularity ε introduced by García-Cuerva and Gatto as special cases. And the (Lᵖ(μ),Lq(μ))-boundedness for fractional integral operators on non-homogeneous metric measure spaces is established. From this, the (Lᵖ(μ),Lq(μ))-boundedness for commutators and multilinear commutators generated by fractional integral operators with RBMO(μ) function are further obtained. These results in this paper includes the corresponding results on both the homogeneous spaces and non-doubling measure spaces.