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

Journal of inequalities and applications

article

Guanghui Lu¹ 

[1] College of Mathematics and Statistics, Northwest Normal University

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

DOI  :  10.1186/s13660-020-02470-1

学科分类：电力

来源: SpringerOpen

【 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.

【 授权许可】

CC BY