Endpoint estimate for maximal commutators with non-doubling measures (Q2495534)

Let \(\mu\) be a Radon measure on \(\mathbb{R}^d\) satisfying the condition \(\mu(B(x,r))\leq C r^n\) for some \(0<n\leq d\), but not necessarily satisfying the doubling condition \(\mu(B(x,2r))\leq C \mu(B(x,r))\). The authors establish the weak type endpoint estimate for the maximal commutators generated by Calderón--Zygmund singular integrals and operators of multiplication by functions belonging to an Orlicz type class associated with \(\mu\).