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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
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