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Peer-reviewedCC BYElectronic Journal of Differential Equations

Generalization of the chord Sobolev inequality for Orlicz spaces

  • Yuke Li1
  • Wentao Guo1
  1. 1Chongqing Technology and Business Univ., China
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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<α<n and α>n.

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Cite

BibTeXRIS
BibTeX
@article{li2026generalization,
  title = {{Generalization of the chord Sobolev inequality for Orlicz spaces}},
  author = {Yuke Li and Wentao Guo},
  journal = {Electronic Journal of Differential Equations},
  year = {2026},
  month = sep,
  url = {http://ejde.math.txstate.edu/Volumes/2026/65/abstr.html},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Generalization of the chord Sobolev inequality for Orlicz spaces
AU  - Yuke Li
AU  - Wentao Guo
PY  - 2026
DA  - 2026/09/01
JO  - Electronic Journal of Differential Equations
UR  - http://ejde.math.txstate.edu/Volumes/2026/65/abstr.html
AB  - 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<α<n and α>n.
SN  - 1072-6691
ER  -