A fractional Moser-Trudinger type inequality in one dimension and its critical points

Abstract

We show a sharp fractional Moser-Trudinger type inequality in dimension 1, i.e. for an interval I b R, p 2 (1, 1) and some1 2 on I. This extends to the fractional case some previous results proven by Adimurthi for the Laplacian and the p-Laplacian operators.Finally with a technique of Ruf we show a fractional Moser-Trudinger inequality on R. MSC 2010. 26A33, 35R11, 35B33.