Abstract
The sharp version of the logarithmic Hardy-Littlewood-Sobolev inequality including the cases of equality is established. We then show that this implies Beckner's generalization of Onofri's inequality to arbitrary dimensions and determines the cases of equality.
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The work of the second author is partially supported by the U.S. National Science Foundation under Grant DMS-90-05729.
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Carlen, E., Loss, M. Competing symmetries, the logarithmic HLS inequality and Onofri's inequality ons n . Geometric and Functional Analysis 2, 90–104 (1992). https://doi.org/10.1007/BF01895706
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DOI: https://doi.org/10.1007/BF01895706