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.