|
|
|
篇目详细内容 |
|
【篇名】 |
On F-Sobolev and Orlicz-Sobolev inequalities |
|
【刊名】 |
Frontiers of Mathematics in China |
|
【刊名缩写】 |
Front. Math. China |
|
【ISSN】 |
1673-3452 |
|
【EISSN】 |
1673-3576 |
|
【DOI】 |
10.1007/s11464-009-0035-3 |
|
【出版社】 |
Higher Education Press and Springer-Verlag |
|
【出版年】 |
2009 |
|
【卷期】 |
4
卷4期 |
|
【页码】 |
659-667
页,共
9
页 |
|
【作者】 |
Cholryong KANG;
Fengyu WANG;
|
|
【关键词】 |
Orlicz-Sobolev inequality; F-Sobolev inequality; super Poincaré inequality |
【摘要】 |
|
Let F ∈ C([0,∞)) be a positive increasing function such that Φ(s) := |s|F(|s|) is a Young function. In general, the F-Sobolev inequality and the Φ-Orlicz-Sobolev inequality are not equivalent. In this paper, a growth condition on F is presented for these two inequalities to be equivalent. The main result generalizes the corresponding known one for F(s) = logδ(1+s) (δ>0). As an application, some criteria are presented for the F-Sobolev inequality to hold. |
|
