Fractional Adams-Moser-Trudinger type inequalities
详细信息 查看全文
- 作者：Luca Martinazzi luca.martinazzi@unibas.ch" class="auth_mail" title="E-mail the corresponding author
- 关键词：Nonlocal equations ; Moser&ndash ; Trudinger inequalities ; Fractional Sobolev spaces
- 刊名：Nonlinear Analysis
- 出版年：2015
- 出版时间：November 2015
- 年：2015
- 卷：127
- 期：Complete
- 页码：263-278
- 全文大小：715 K
文摘
Extending several works, we prove a general Adams–Moser–Trudinger type inequality for the embedding of Bessel-potential spaces 
into Orlicz spaces for an arbitrary domain 惟 with finite measure. In particular we prove
for a positive constant 伪n,p whose sharpness we also prove. We further extend this result to the case of Lorentz-spaces (i.e. ). The proofs are simple, as they use Green functions for fractional Laplace operators and suitable cut-off procedures to reduce the fractional results to the sharp estimate on the Riesz potential proven by Adams and its generalization proven by Xiao and Zhai.
into Orlicz spaces for an arbitrary domain 惟 with finite measure. In particular we prove). The proofs are simple, as they use Green functions for fractional Laplace operators and suitable cut-off procedures to reduce the fractional results to the sharp estimate on the Riesz potential proven by Adams and its generalization proven by Xiao and Zhai.We also discuss an application to the problem of prescribing the Q-curvature and some open problems.