Title: A Harmonic Analysis perspective on $W^{s,p}$ as $s \to 1^-$.

Abstract: We revisit the Bourgain-Brezis-Mironescu result that the Gagliardo-Norm of the fractional Sobolev space W^{s,p}, up to rescaling, converges to W^{1,p} as s\to 1. We do so from the perspective of Triebel-Lizorkin spaces, by finding sharp $s$-dependencies for several embeddings between $W^{s,p}$ and $F^{s,p}_q$ where $q$ is either 2 or $p$. We recover known results, find a few new estimates, and discuss some open questions.
Joint work with Denis Brazke, Po-Lam Yung.