Submitted:
27 April 2026
Posted:
28 April 2026
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Abstract
In this paper, we studied the limiting cases of $\alpha \to n^-$ and $\alpha \to 0^+$ in the affine Hardy-Littlewood-Sobolev (HLS) inequalities proved in [25]. To be specific, we established affine logarithmic HLS inequalities and affine Beckner-type logarithmic Sobolev inequalities with respect to two different functions.
Keywords:
logarithmic HLS inequalities
; affine HLS inequalities
; Riesz’s rearrangement inequalities
; dual mixed volumes
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