The maximal smoothing effect of dispersive equations

Toshihiko Hoshiro Himeji Institute of Technology

In this talk, we discuss some smoothing estimates of the initial value problem for dispersive equations. We consider the initial value problem of the form: idu/dt + P (D)u = f(t, x), and u(0, x) = u_{0}(x). We will show that, for the maximal smoothing in space-time, it is necessary and sufficient that the principal part of the symbol does not vanish on the unit sphere.