On F-Sobolev and Orlicz-Sobolev inequalities

doi:10.1007/s11464-009-0035-3

Front. Math. China

2009, Vol. 4

Issue (4) : 659-667 https://doi.org/10.1007/s11464-009-0035-3

Research articles

On F-Sobolev and Orlicz-Sobolev inequalities

Cholryong KANG¹,Fengyu WANG²,

1.School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China；Department of Mathematics and Mechanics, University of Science, Pyongyang, D. P. R. of Korea; 2.School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China；Department of Mathematics, Swansea University, Singleton Park, Swansea, SA2 8PP, UK;

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Abstract Let F ∈ C([0,∞)) be a positive increasing function such that Φ(s) := sF(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) = log^δ(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 Poincar&#233 inequality

Issue Date: 05 December 2009

Cite this article:

Cholryong KANG,Fengyu WANG. On F-Sobolev and Orlicz-Sobolev inequalities[J]. Front. Math. China, 2009, 4(4): 659-667.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-009-0035-3
https://academic.hep.com.cn/fmc/EN/Y2009/V4/I4/659

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