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- Title
Commutators of fractional maximal operator in variable Lebesgue spaces over bounded quasi‐metric measure spaces.
- Authors
Guliyev, Vagif S.; Samko, Stefan G.
- Abstract
We study the fractional maximal commutators Mb,η$$ {M}_{b,\eta } $$ and the commutators [b,Mη]$$ \left[b,{M}_{\eta}\right] $$ of the fractional maximal operator with b∈BMO(X)$$ b\in BMO(X) $$ in the variable Lebesgue spaces Lp(·)(X)$$ {L}^{p\left(\cdotp \right)}(X) $$ over bounded quasi‐metric measure spaces. We give necessary and sufficient conditions for the boundedness of the operators Mb,η$$ {M}_{b,\eta } $$ and [b,Mη]$$ \left[b,{M}_{\eta}\right] $$ on the spaces Lp(·)(X)$$ {L}^{p\left(\cdotp \right)}(X) $$ when b∈BMO(X)$$ b\in BMO(X) $$. Furthermore, we obtain some new characterizations for certain subspaces of BMO(X)$$ BMO(X) $$.
- Subjects
QUASI-metric spaces; COMMUTATION (Electricity); COMMUTATORS (Operator theory); MAXIMAL functions
- Publication
Mathematical Methods in the Applied Sciences, 2022, Vol 45, Issue 16, p9266
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.8303