Abstract. In this paper, we provide a characterization of a large class of transportation-cost inequalities in terms of exponential integrability of the cost function under the reference probability measure. Our results completely extend the previous works by Djellout, Guillin and Wu (DGW03) and Bolley and Villani (BV03).
Nathael Gozlan. "Integral criteria for transportation cost inequalities." Electron. Commun. Probab. 11 64 - 77, 2006. https://doi.org/10.1214/ECP.v11-1198