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arXiv · 1308.5483

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

Rulong Xie·Lisheng Shu
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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 $α$ and regularity $ε$ introduced by García-Cuerva and Gatto as special cases. And the $(L^{p}(μ),L^{q}(μ))$-boundedness for fractional integral operators on non-homogeneous metric measure spaces is established. From this, the $(L^{p}(μ),L^{q}(μ))$-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.

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Rulong Xie, Lisheng Shu. 2013-09-26. Boundedness of fractional integral operators on non-homogeneous metric measure spaces. https://arxiv.org/abs/1308.5483

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