Pieroe D'Ancona (Rome)

Estimates with higher angular integrability and applications

I will talk about recent work with R.Luca' on estimates for fractional integrals with different integrability properties in the radial and angular directions. Using these fundamental block several classical estimates can be improved: Sobolev embeddings, Caffarelli-Kohn- Nirenberg estimates, Strichartz estimates for the wave equation. As an example we apply the estimate to refine a regularity result of Serrin type for the Navier-Stokes equation.