Some notes on commutators of the fractional maximal function on variable Lebesgue spaces

Pu Zhang, Zengyan Si, Jianglong Wu

Let $0<\alpha <n$ and $M_{\alpha }$ be the fractional maximal function. The nonlinear commutator of $M_{\alpha }$ and a locally integrable function $b$ is given by $[b,M_{\alpha }](f)=b{M}_{\alpha }(f)-M_{\alpha }(bf)$. In this…