Extremals for Fractional Moser–Trudinger Inequalities in Dimension 1 via Harmonic Extensions and Commutator Estimates

Abstract

We prove the existence of extremals for fractional Moser–Trudinger inequalities in an interval and on the whole real line. In both cases we use blow-up analysis for the corresponding Euler–Lagrange equation, which requires new sharp estimates obtained via commutator techniques.

Keywords

• moser–trudinger
• fractional laplacian
• extremals
• blow-up
• commutator estimates
• 35r11
• 35b44
• 35j61
• 35j08