Generalization of the chord Sobolev inequality for Orlicz spaces

Abstract

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: \(0<\alphan\).  For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2026/65/abstr.html