In this talk I will explore the limiting case $\gamma\to(1/2)^-$ in dimension one for the fractional Caffarelli-Kohn-Nirenberg inequality, obtaining Onofri's inequality in the unit disk as a limit. An important aspect is the study of solutions of the weighted Liouville equation for the half-Laplacian in dimension one.
This is joint work with Maria del Mar Gonzalez and Ali Hyder.
