The relationship between the classical chord power integrals and radial mean bodies, as well as the classical chord Sobolev inequalities, have already been established. This article extends the concepts of chord power integrals and chord Sobolev inequalities to the Orlicz space framework. We provide the definitions of the Orlicz chord power integrals and the Orlicz radial mean bodies, and we establish their equivalence. We prove the Orlicz chord Sobolev inequality for two distinct cases: \(0<\alpha
Submitted April 28, 2026. Published September 3, 2026.
Math Subject Classifications: 26D20, 46E30.
Key Words: Orlicz function; Orlicz chord power integral; Orlicz radial mean body; Orlicz chord Sobolev inequality.
DOI: 10.58997/ejde.2026.65
Show me the PDF file (399 KB), TEX file for this article.
 |
Yuke Li School of Mathematics and Statistics Chongqing Technology and Business University Chongqing, 400067, China email: liyuke1@ctbu.edu.cn |
|---|---|
 |
Wentao Guo School of Mathematics and Statistics Chongqing Technology and Business University Chongqing, 400067, China email: guowentao@ctbu.edu.cn |
Return to the EJDE web page