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On F-Sobolev and Orlicz-Sobolev inequalities |
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| Authors: | Cholryong Kang Fengyu Wang |
| Affiliation: | 1.School of MathematicalSciences, Beijing Normal University, Beijing 100875, China；Department of Mathematicsand Mechanics, University of Science, Pyongyang, D. P. R. of Korea; 2.School of MathematicalSciences, Beijing Normal University, Beijing 100875, China；Department of Mathematics,Swansea University, Singleton Park, Swansea, SA2 8PP, UK; |
| Abstract: | 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. |
| Keywords: | Orlicz-Sobolev inequality F-Sobolev inequality super Poincaré inequality |
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