Title: Monge-Ampère equations with drifts for certain end-point estimates in Harmonic Analysis
Abstract: We will show a several instances when an end-point estimate in Harmonic Analysis can be matched with an estimate of a solution of a Monge-Ampère equation with various drift. On certain occasions (with certain drifts, domains, and boundary conditions) the corresponding solution can be estimated, or even found, which immediately gives the result for an underlying Harmonic Analysis problem.