  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 Schrodinger equation in
R^{2+1} we obtain the sharp global space-time estimates with optimal regularity
from the previous known local ones.
