Some notes on commutators of the fractional maximal function on variable Lebesgue spaces
Abstract Let 0<α<n $0<\alpha<n$ and Mα $M_{\alpha}$ be the fractional maximal function. The nonlinear commutator of Mα $M_{\alpha}$ and a locally integrable function b is given by [b,Mα](f)=bMα(f)−Mα(bf) $[b,M_{\alpha}](f)=bM_{\alpha}(f)-M_{\alpha}(bf)$. In this paper, we mainly give som...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-01-01
|
| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-019-1960-7 |
| Summary: | Abstract Let 0<α<n $0<\alpha<n$ and Mα $M_{\alpha}$ be the fractional maximal function. The nonlinear commutator of Mα $M_{\alpha}$ and a locally integrable function b is given by [b,Mα](f)=bMα(f)−Mα(bf) $[b,M_{\alpha}](f)=bM_{\alpha}(f)-M_{\alpha}(bf)$. In this paper, we mainly give some necessary and sufficient conditions for the boundedness of [b,Mα] $[b,M_{\alpha}]$ on variable Lebesgue spaces when b belongs to Lipschitz or BMO(Rn) $\mathit{BMO}({\mathbb{R}}^{n})$ spaces, by which some new characterizations for certain subclasses of Lipschitz and BMO(Rn) $\mathit{BMO}({\mathbb{R}}^{n})$ spaces are obtained. |
|---|---|
| ISSN: | 1029-242X |