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Jul 6, 2017 at 15:23 comment added Denis Serre Just to mention that I have know a proof of the general inequality. The proof follows about the same ideas as that of Gagliardo. It is just more cumbersome.
Mar 1, 2017 at 20:24 comment added Liviu Nicolaescu Have you checked Brascamp-Lieb inequality? en.wikipedia.org/wiki/Brascamp%E2%80%93Lieb_inequality
Mar 1, 2017 at 18:26 comment added Willie Wong Just to be clear: are you worried about measure theoretic difficulties? If you assume all functions are, say, in Schwartz space, then what you want follows from Holder in each variable taking into account that the number of subsets of $\{1, \ldots, d\}$ of length $k$ that contains a given element $\{1\}$ is exactly $d-1$ choose $k-1$. Am I missing something?
Mar 1, 2017 at 15:58 history asked Denis Serre CC BY-SA 3.0