Abstract :We study the limiting case in dimension one for the fractional Caffarelli-Kohn-Nirenberg inequality, obtaining Onofri’s inequality in the unit disk as a limit. One difficulty here is the lack of an explicit expression for the extremal. 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 A. Hyder (TIFR Bangalore) and M. Saez (U. Pontificia Chile).

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