We prove the existence of extremals for fractional Moser-Trudinger inequalities in an interval and on thewhole real line. In both caseswe use blow-up analysis for the corresponding Euler-Lagrange equation, which requires new sharp estimates obtained via commutator techniques.
Extremals for Fractional Moser-Trudinger Inequalities in Dimension 1 via Harmonic Extensions and Commutator Estimates
Mancini G.;Martinazzi L.
2020
Abstract
We prove the existence of extremals for fractional Moser-Trudinger inequalities in an interval and on thewhole real line. In both caseswe use blow-up analysis for the corresponding Euler-Lagrange equation, which requires new sharp estimates obtained via commutator techniques.
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