Oscar Dominguez

A famous result by Bourgain--Brezis--Mironescu (BBM) asserts that standard Sobolev spaces can be recovered by taking limits of certain normalizations of the Gagliardo seminorms. In this talk, we show that these normalizations are not specific to Sobolev spaces, but they are part of a rather general phenomenon based on interpolation/extrapolation theory. This abstract perspective enables us to obtain BBM for fractional Sobolev spaces via new extensions of the classical Gagliardo seminorms: the so-called Butzer seminorms. This is joint work with Mario Milman.