Commutators of θ -type generalized fractional integrals on non-homogeneous spaces

[摘要] The aim of this paper is to establish the boundednes of the commutator $[b,T_{\alpha }]$ generated by θ-type generalized fractional integral $T_{\alpha }$ and $b\in \widetilde{\mathrm{RBMO}}(\mu )$ over a non-homogeneous metric measure space. Under the assumption that the dominating function λ satisfies the ϵ-weak reverse doubling condition, the author proves that the commutator $[b,T_{\alpha }]$ is bounded from the Lebesgue space $L^{p}(\mu )$ into the space $L^{q}(\mu )$ for $\frac{1}{q}=\frac{1}{p}-\alpha $ and $\alpha \in (0,1)$ , and bounded from the atomic Hardy space $\widetilde{H}^{1}_{b}(\mu )$ with discrete coefficient into the space $L^{\frac{1}{1-\alpha },\infty }(\mu )$ . Furthermore, the boundedness of the commutator $[b,T_{\alpha }]$ on a generalized Morrey space and a Morrey space is also got.

[学科分类] 电力

[关键词] Non-homogeneous metric measure space;θ -type generalized fractional integral;Commutator;\(\widetilde{\mathrm{RBMO}}(\mu )\);Hardy space \(\widetilde{H}^{1}_{b}(\mu )\)