• East Asian mathematical journal
• /
• v.33 no.1
• /
• pp.103-113
• /
• 2017

We provide quantitative two weight estimates for the commutator of the Hilbert transform under certain conditions on a pair of weights (u, v) and b in $Carl_{u,v}$. In [10] and [11], Bloom's inequality is shown in a modern setting, and the boundedness of the commutators is provided by assuming both weights u, v are $A_2$ and $b{\in}BMO_{\rho}$. In the present paper we show that the condition on b can be replaced by $Carl_{u,v}$ by using the joint $A^d_2$ condition.