Nonhomogeneous $T(1)$ Theorem on Product Quasimetric Spaces

In this paper, we provide a non-homogeneous $T(1)$ theorem on product spaces $(X_1 \times X_2, \rho_1 \times \rho_2, \mu_1 \times \mu_2)$ equipped with a quasimetric $\rho_1 \times \rho_2$ and a Borel measure $\mu_1 \times \mu_2$, which, need not be doubling but satisfies an upper control on the size of quasiballs.