Weighted estimates for commutators of singular integral operators with non-doubling measures

Abstract

Let μ be a nonnegative Radon measure on ℝd which only satisfies μ(B(x, r)) ⩽ C0rn for all x ∈ ℝd, r > 0, and some fixed constants C0 > 0 and n ∈ (0, d]. In this paper, some weighted weak type estimates with \(A_{p, (\log L)^\sigma }^\rho \) (μ) weights are established for the commutators generated by Calderon-Zygmund singular integral operators with RBMO(μ) functions.