Strichartz estimates for the Schroedinger and heat equations perturbed with singular and time dependent potentials

摘要

We prove Strichartz estimates for the Schroedinger equation perturbed with a small time dependent potential V(t, x) belonging to the weak Lebesgue space L_t~∞L_x~((n/2,∞)). We also consider the heat equation perturbed with a time independent singular potential V(x) ∈ L~((n/2,∞)) and we prove both the maximum principle and the Strichartz estimates under a suitable smallness condition on the negative part of the potential.