Stability of some Fractional function spaces

Fractional Sobolev spaces, which generalize the concept of classical Sobolev spaces, have been a central tool in harmonic analysis, variation problems, and PDE for several decades. One of the main issues of these spaces is that they are unstable as the fractional parameter s goes to 1. In this talk, I will share some of the new results that I've obtained regarding stabilizing these spaces, and how these results compare to the classical Bourgain-Brezis- Mironescu formula.