Endpoint estimates for commutators of singular integral operators associated with admissible functions

Let $(\mathcal X, d, μ)$ be a space of homogeneous type and let $ρ$ be an admissible function on $\mathcal X$. In this paper, we introduce a new class of singular integral operators associated with $ρ$, including a wide range of operators arising in harmonic analysis. For such an operator $T$ and a