Abstract
Under the assumption that µ is a non-doubling measure on Rd, the authors obtain the (Lp, Lq)-boundedness and the weak type endpoint estimate for the multilinear commutators generated by fractional integrals with RBMO(µ) functions of Tolsa or with Oscexp Lr (µ) functions for r ≥ 1, where Oscexp Lr (µ) is a space of Orlicz type satisfying that Oscexp Lr (µ) = RBMO(µ) if r = 1 and Oscexp Lr (µ) ⊂ RBMO(µ) if r >
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