Generalized Calderón-Zygmund operators on the Hardy space $H_{\rho }^1(\mathcal{X})$

Let $(\mathcal{X},d,\mu )$ be an RD-space, and let $\rho$ be an admissible function on $\mathcal{X}$. We establish necessary and sufficient conditions for the boundedness of a new class of generalized Calderón-Zygmund operators of log-Dini type on the Hardy space $H_{\rho }^1(\mathcal{X})$, introduced by Yang and Zhou. Our results extend and unify some recent results, providing further insights into the study of singular integral operators in this setting.