Extended Strichartz estimates for the heat equation with a Strichartz type potential.

We present new extended Strichartz estimates for the solutions to the heat equation, perturbed with a time dependent potential V : ℝ+ ℝd → ℝ, satisfying appropriate space and time integrability conditions (i.e. bounded with respect to some La(I, Lb(ℝd)) norms). We focus ourselves to the case with initial datum in Hσ, σ ∈ (0, 1] and d ≥ 1. Some applications of these new estimates are also displayed. [ABSTRACT FROM AUTHOR]