enter image description here Where could I find the 1st appearance in the community for the Fenchel-Young inequality?

  • $\begingroup$ Are you asking about the term "Fenchel-Young inequality" (as opposed, say, to "Fenchel inequality", or to the fact it names? What is "the community" here? A group of people, or the printed literature? $\endgroup$ Jan 21, 2018 at 2:09

1 Answer 1


Rockafellar's fundamental "Convex Analysis" points to the following article from 1949, where the inequality is stated (although with outdated notation):

There the author regards the inequality as a generalization of the inequality of Young, which only covers the scalar, differentiable case as far as I understand. No references to previous occurrences of this result are given by Fenchel, so my guess is that the above reference is its first appearance.

For Young's inequality, from the above reference one reaches:

  • G. H. Hardy, J. E. Littlewood, G. Pôlya, "Inequalities," Cambridge (1934).
  • W. H. Young, "On classes of summable functions and their Fourier series," Proc. Royal Soc. (A), 87, pp. 225-229 (1912).
  • $\begingroup$ This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review $\endgroup$ Jan 21, 2018 at 12:16
  • $\begingroup$ The way I interpreted the question (and most importantly: the title) mine is a perfectly honest tentative answer. Conversly, I don't see how my post can be regarded as critique or request for clarification. $\endgroup$ Jan 21, 2018 at 12:22
  • $\begingroup$ Answers such as yours (which just provide a reference) are considered here as inappropriate. They should be comments intead. $\endgroup$ Jan 21, 2018 at 12:25
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    $\begingroup$ I see. I added some context that explains how I obtained the reference and that could help finding more accurate answers (that is, older occurrences of the result, in case there are). $\endgroup$ Jan 21, 2018 at 13:19

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