A global space-time estimate for dispersive operators through its local estimate

Abstract

We will show that a local space-time estimate implies a global space-time estimate for dispersive operators. In order for this implication we consider a Littlewood-Paley type square function estimate for dispersive operators in a time variable and a generalization of Tao's epsilon removal lemma in mixed norms. By applying this implication to the fractional Schrödinger equation in R2+1 we obtain the sharp global space-time estimates with optimal regularity from the previous known local ones.