Generalized affine Hardy-Littlewood-Sobolev inequalities
Youjiang Lin, Jinghong Zhou, Jiaming Lan
TL;DR
This paper introduces a stronger affine Hardy-Littlewood-Sobolev inequality involving two functions and establishes reverse inequalities for log-concave functions, advancing the theoretical understanding of integral inequalities.
Contribution
It develops a generalized affine Hardy-Littlewood-Sobolev inequality that improves upon the classical version and proves reverse inequalities for log-concave functions.
Findings
Established a stronger affine Hardy-Littlewood-Sobolev inequality.
Proved reverse inequalities for log-concave functions.
Enhanced theoretical framework for integral inequalities.
Abstract
We establishe an affine Hardy-Littlewood-Sobolev inequality concerning two different functions which is stronger than the classical Hardy-Littlewood-Sobolev inequality. Furthermore, we also prove reverse inequalities for the new inequalities for log-concave functions.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Point processes and geometric inequalities · Advanced Harmonic Analysis Research