Affine Logarithmic HLS and Beckner-Type Logarithmic Sobolev Inequalities

2025/04/12 by Cai, Xiaxing · 2 citations
#FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2504.09251

Abstract

In this paper, we consider two limiting cases (α→ n and α→ 0 ) of the recent affine HLS inequalities by Haddad and Ludwig. As α→ n, the affine logarithmic HLS inequality is established, which is stronger than the logarithmic HLS inequality by Carlen and Loss from 1992 and Beckner from 1993. As α→ 0, an affine version of Beckner's logarithmic Sobolev inequality is established, which is also a limiting case of the affine fractional L² Sobolev inequalities. The affine logarithmic Sobolev inequality is stronger than the original version by Beckner from 1995.

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