Strichartz estimates via the Schrodinger maximal operator

We consider the Schrodinger operator e(it Delta) acting on initial data f in (H) over dot(s). We show that an affirmative answer to a question of Carleson, concerning the sharp range of s for which lim(t -> 0) e(it Delta) f (x) = f (x) a.e.x. is an element of R(n), would imply an affirmative answer to a question of Planchon, concerning the sharp range of q and r for which e(it Delta) is bounded in L(x)(q) (R(n), L(t)(r) (R)). When n = 2, we unconditionally improve the range for which the mixed norm estimates hold.