Critical and subcritical fractional Trudinger-Moser type inequalities on ℝ

2017/02/27 by Takahashi, Futoshi
#26D10 #35A23 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1702.08206

Abstract

In this paper, we are concerned with the critical and subcritical Trudinger-Moser type inequalities for functions in a fractional Sobolev space H^1/2,2 on the whole real line. We prove the relation between two inequalities and discuss the attainability of the suprema.

Related

• Weighted Trudinger-Moser inequalities in the subcritical Sobolev spaces and their applications
• Extremals for fractional Moser-Trudinger inequalities in dimension 1 via\n harmonic extensions and commutator estimates
• A new proof of subcritical Trudinger-Moser inequalities on the whole Euclidean space
• Equivalence of critical and subcritical sharp Trudinger-Moser-Adams inequalities
• On the Moser-Trudinger inequality in fractional Sobolev-Slobodeckij spaces