On a stochastic Hardy-Littlewood-Sobolev inequality with application to Strichartz estimates for the white noise dispersion

Abstract

In this paper, we investigate a stochastic Hardy-Littlewood-Sobolev inequality. Due to the stochastic nature of the inequality, the relation between the exponents of intgrability is modified. This modification can be understood as a regularization by noise phenomenon. As a direct application, we derive Strichartz estimates for the white noise dispersion which enables us to address a conjecture from [3].