Accepted Paper

Inserted: 21 nov 2021
Last Updated: 22 dec 2022

Journal: Journal d'Analyse Mathématique
Year: 2022
Doi: 10.1007/s11854-022-0234-3

Abstract:

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.