Remarks on the fractional Moser-Trudinger inequality

Abstract

In this article, we study the connection between the fractional Moser-Trudinger inequality and the fractional $\left(\frac{kp}{p-1},p\right)$-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.

20 pages, to appear

References in corpus (4)

• Fractional Adams-Moser-Trudinger type inequalities
• The singular Moser- Trudger Inequality on simply connected domains
• Study of fractional Poincaré inequalities on unbounded domains
• Fractional Poincaré Inequality for Unbounded Domains with Finite Ball Condition: Counter Example