"Endpoint Fourier restriction and unrectifiability"

Abstract: In this talk we show that if a measure of dimension s on R^d admits a (p,q) Fourier restriction estimates for the endpoint exponent allowed by its dimension, namely q=sp'/d then a dichotomy holds: either the measure is absolutely continuous or it is supported on a purely 1-unrectifiable set.
If time permits, I will explain how the same techniques can be used to study the structure of possible counterexamples to the David-Semmes conjecture on the rectifiability of good measures for the Riesz transform.
Based on joint works with Giacomo Del Nin.

Eventi passati

È possibile consultare gli eventi del precedente ciclo alla pagina dedicata