Haddad, J. E., & Ludwig, M. (2025). Affine Hardy–Littlewood–Sobolev inequalities. Journal of the European Mathematical Society. https://doi.org/10.4171/jems/1648
E104-06 - Forschungsbereich Konvexe und Diskrete Geometrie
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Journal:
Journal of the European Mathematical Society
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ISSN:
1435-9855
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Date (published):
28-May-2025
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Publisher:
European Mathematical Society - EMS - Publishing House GmbH
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Peer reviewed:
Yes
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Keywords:
affine Hardy-Littlewood-Sobolev inequality; radial mean body
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Abstract:
Sharp affine Hardy–Littlewood–Sobolev inequalities for functions on Rⁿ are established, which are significantly stronger than (and directly imply) the sharp Hardy–Littlewood–Sobolev inequalities by Lieb and by Beckner, Dou, and Zhu. In addition, sharp reverse inequalities for the new inequalities and the affine fractional L² Sobolev inequalities are obtained for log-concave functions on Rⁿ.
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Project title:
Anisotrope fraktionelle Perimeter und Riesz-Energien: P 37030-N (FWF - Österr. Wissenschaftsfonds)
