Answers are grounded in this paper and cite their sources.
Establishes affine logarithmic inequalities in limiting cases, extending classical results to a new framework.
In this paper, we studied the limiting regimes α→n− and α→0+ in the affine Hardy–Littlewood–Sobolev (HLS) inequalities. Specifically, we established affine logarithmic HLS inequalities and affine Beckner-type logarithmic Sobolev inequalities for pairs of functions. The results extended classical logarithmic inequalities to the affine setting and recovered known sharp inequalities in the limiting cases.
No takes yet. Share an insight, caveat, or question.
Lin et al. (2026) studied this question.
Synapse has enriched 10 related papers. Consider them for comparative context: