Strichartz estimates for Schrödinger equations in weighted l² spaces and their applications

We obtain weighted L² Strichartz estimates for Schrödinger equations i_tu + (-Δ)^a-2u = F(x; t), u(x; 0) = f(x), of general orders a > 1 with radial data f; F with respect to the spatial variable x, whenever the weight is in a Morrey-Campanato type class. This is done by making use of a useful property of maximal functions of the weights together with frequency-localized estimates which follow from using bilinear interpolation and some estimates of Bessel functions. As consequences, we give an affirmative answer to a question posed in [1] concerning weighted homogeneous Strichartz estimates, and improve previously known Morawetz estimates. We also apply the weighted L² estimates to the well-posedness theory for the Schrödinger equations with time-dependent potentials in the class.