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

Abstract

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 $\alpha$ and regularity $\epsilon$ introduced by García-Cuerva and Gatto as special cases. And the $(L^p(\mu ),L^q(\mu ))$-boundedness for fractional integral operators on non-homogeneous metric measure spaces is established. From this, the $(L^p(\mu ),L^q(\mu ))$-boundedness for commutators and multilinear commutators generated by fractional integral operators with $RBMO(\mu )$ function are further obtained. These results in this paper includes the corresponding results on both the homogeneous spaces and non-doubling measure spaces.

26 pages

References in corpus (2)

• The Hardy Space $H^1$ on Non-homogeneous Metric Spaces
• Spaces of Type BLO on Non-homogeneous Metric Measure Spaces