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A note on commutators of fractional integrals with $$\text{RBMO}(\mu)$$ functions. (English) Zbl 1033.42008
Let $$\mu$$ be a Borel measure on $${\mathbb R}^{d}$$ which may be non-doubling, but satisfies $$\mu (Q)\leq \text{cl}(Q)^{n}$$ for all cubes $$Q$$ with sides parallel to the coordinate axes and for a fixed $$n$$ with $$0<n\leq d$$. In this note the authors consider the commutators of fractional integrals with functions of the new BMO introduced by X. Tolsa [ Math. Ann. 319, 89–149 (2001; Zbl 0974.42014)].

##### MSC:
 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25 Maximal functions, Littlewood-Paley theory
##### Keywords:
BMO; commutator; non-doubling measures
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