Inhomogeneous Strichartz estimates for Schrödinger's equation

Abstract

Foschi and Vilela in their independent works (\cite{F},\cite{V}) showed that the range of $(1/r,1/\tilde{r})$ for which the inhomogeneous Strichartz estimate $\Vert {\int }_0^t{e}^{i(t-s)\Delta }F(\cdot ,s)ds{\Vert }_{L_t^q{L}_x^r}\lesssim \Vert F{\Vert }_{L_t^{{\tilde{q}}^{\prime }}{L}_x^{{\tilde{r}}^{\prime }}}$ holds for some $q,\tilde{q}$ is contained in the closed pentagon with vertices $A,B,B^{\prime },P,P^{\prime }$ except the points $P,P^{\prime }$ (see Figure 1). We obtain the estimate for the corner points $P,P^{\prime }$.

To appear in J. Math. Anal. Appl., 10 pages

References in corpus (1)

• Time decay for the bounded mean oscillation of solutions of the Schrödinger and wave equations