Inserted: 21 nov 2021
Journal: Journal d'Analyse Mathématique
In this article, we study the connection between the fractional Moser-Trudinger inequality and the fractional (kpp−1,p)-Poincaré type inequality for any Euclidean domain and discuss the sharpness of this inequality whose analogous results are well known in the local case. We further provide sufficient conditions on domains for fractional (q,p)-Poincaré type inequalities to hold. We also derive Adachi-Tanaka type inequalities in the non-local setting.