Abstract
In this article, we define and we study the Hardy spaces associated with the Weinstein operator. We establish refined Sobolev inequalities between the homogeneous Weinstein-Besov spaces and many spaces, as the homogeneous Weinstein-Riesz spaces and the generalized Lorentz spaces. Next we prove Hardy-type inequalities in the homogeneous Weinstein-Besov space, homogeneous Weinstein-Riesz space, and Weinstein-Hardy space