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

Abstract

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.