Strichartz estimates for the Schrödinger propagator in Wiener amalgam spaces

Abstract

In this paper we study the Strichartz estimates for the Schrödinger propagator in the context of Wiener amalgam spaces which, unlike the Lebesgue spaces, control the local regularity of a function and its decay at infinity separately. This separability makes it possible to perform a finer analysis of the local and global behavior of the propagator. Our results improve some of the classical ones in the case of large time.

Strichartz estimates for the Dirac flow in Wiener amalgam spaces

“…This separability makes it possible to perform a finer analysis of the local and global behavior of the flow. These aspects were originally pointed out in the several works by Cordero and Nicola [2–4] in the context of the Schrödinger flow $$\text{e}^{\text{i}t\Delta }$$, and the works were generalized in [11] to initial data with regularity. See also [12] for the wave flow $$\text{e}^{\text{i}t\sqrt {-\Delta }}$$.…”

Strichartz estimates for the Dirac flow in Wiener amalgam spaces

“…This separability makes it possible to perform a finer analysis of the local and global behavior of the flow. These aspects were originally pointed out in the several works by Cordero and Nicola ([2,3,4]) in the context of the Schrödinger flow e it∆ , and the works were generalized in [11] to initial data with regularity. See also [12] for the wave flow e it √ −∆ .…”