Multilinear commutators of singular integrals with non doubling measures (Q1773041)

Let \(\mu\) be a Radon measure on \({\mathbb R}^d\) that satisfies the condition \(\mu(B(x,r))\leq C r^n\) for some \(0<n\leq d\), but which may not satisfy the doubling condition \(\mu(B(x,2r))\leq C \mu(B(x,r))\). The aim of this paper is, if \(1<p<\infty\), to prove the \(L^p(\mu)\) boundedness for multilinear commutators \([b_k,\dots,[b_1,T]]\) generated by a Calderón-Zygmund operator \(T\) combined with functions \(b_i\) belonging to the class \(RBMO(\mu)\) introduced by \textit{X. Tolsa} [Math. Ann. 319, 269--304 (2001; Zbl 0945.30032)]. The endpoint case is also considered and a weak type estimate is obtained for commutators generated by \(T\) and functions \(b_i\) belonging to an Orlicz type class associated with \(\mu\).