Frontiers of Mathematics in China >

2009 , Vol. 4 >Issue 4: 659 - 667

DOI: https://doi.org/10.1007/s11464-009-0035-3

Research articles

On F-Sobolev and Orlicz-Sobolev inequalities

Expand
  • 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;

Published date: 05 Dec 2009

Fold

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) = logδ(1+s) (δ>0). As an application, some criteria are presented for the F-Sobolev inequality to hold.

Key words： Orlicz-Sobolev inequality; F-Sobolev inequality; super Poincaré inequality

Cite this article

Cholryong KANG, Fengyu WANG, . On F-Sobolev and Orlicz-Sobolev inequalities[J]. Frontiers of Mathematics in China, 2009 , 4(4) : 659 -667 . DOI: 10.1007/s11464-009-0035-3

Options
Outlines

/

〈 〉