Affine logarithmic HLS and Beckner-type logarithmic Sobolev inequalities
Abstract
In this paper, we consider two limiting cases ( α → n and α → 0 ) of the affine HLS inequalities introduced by Haddad and Ludwig. We establish an affine logarithmic HLS inequality and an affine version of Beckner's logarithmic Sobolev inequality, both of which are stronger than their classical counterparts — namely, the logarithmic HLS inequality of Carlen and Loss (1992) and Beckner (1993), and Beckner's logarithmic Sobolev inequality (1995). For both inequalities, we obtain sharp constants together with a complete characterization of all equality cases.
Fields of Study & Subjects
Fatigue and fracture mechanics
Publication details
- Journal / source
- Journal of Functional Analysis
- Volume
- 291
- Issue
- 9
- Pages
- 111603–111603
- Publication date
- 11 June 2026
- Language
- EN