We offer a lateral approach to trace inequalities for potential-type operators based on an appropriate modification of Calderón interpolation theorem. We develop a general theoretical tool for establishing boundedness of notoriously difficult operators (such as potentials) on certain specific types of rearrangement-invariant function spaces from analogous properties of operators that are easier to handle (such as fractional maximal operators). The key ingredient for the development of the theory is the initial pair of endpoint estimates for the easier operator whose pivotal example is based on a two-weight inequality of Sawyer. Among various applications, we obtain a generalization of the celebrated trace inequality involving the Riesz potential and the Hausdorff content by Korobkov and Kristensen. 

This is a joint work with Zdenek Mihula of Prague and Daniel Spector of Taipei.