Weak Type Estimates forCommutators and Multilinear Commutators of Marcinkiewicz Integrals With Non-doubling Measures

Let µ be a nonnegative Radon measure on R d which only satisfies the growth condition µ(B(x,r)) C0r n for all x 2 R d and r > 0, where C0 is a fixed constant and 0 < n d. The purpose of this paper is to establish the boundedness from L(logL) 1 r (µ) to weak L 1 (µ) for the commutators and the multilinear commutators generated by Marcinkiewicz