Abstract:

I will begin with a discussion of sharp constants and extremisers for L^p space-time estimates (or Strichartz estimates) for solutions of the homogeneous Schrodinger and wave equations with initial data in L^2 or, more generally, certain Sobolev spaces. The majority of my talk will concern such sharpness considerations for certain weighted L^2 space-time estimates (or smoothing estimates) in which case we may consider a larger class of dispersive equations.