English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

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.

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