BCAM Scientific Seminar: Stability of sharp Fourier restriction to spheres

TIME: 10:30-11:30
LOCATION: Seminar Room at BCAM

Abstract
In dimension $din{3, 4, 5, 6, 7}$, we establish that the constant functions maximize the weighted $L2(S{d-1}) L4(Rd)$ Fourier extension estimate on the sphere, provided that the weight function is sufficiently regular and small, in a proper and effective sense. This extends the known result in the unweighted case. One of the main tools is an integration by parts identity, which generalizes the so-called "magic identity" of Foschi for the unweighted inequality with $d=3$ (that is, the classical Stein Tomas estimate). Joint work with E.Carneiro and D.Oliveira e Silva.