Mixed-norm estimates for the free Schrodinger equation
Speaker:
Keith Rogers, Universidad Autónoma de Madrid
Date and Time:
Thursday, February 21, 2008 - 10:00am to 10:45am
Location:
Fields Institute, Room 230
Abstract:
We consider when the Schr¨odinger operator e
it∆ is bounded from H˙ s
(R
n
) to L
q
x
(R
n
, Lr
t
(R)).
When q > r, the Sobolev index s can be negative. For n ≥ 5, we find the sharp range of
such estimates up to endpoints. When q < r, we prove that the sharp estimates would
follow if the maximal operator sup0<t<1
|e
it∆f| were bounded from H1/4
(R
n
) to L
2
loc(R
n
).
