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A detail in Kato's paper (Strong $L^p$-Solutions of the Navier-Stokes Equation in $\mathbb R^m$, with Applications to Weak Solution).

Here is the link: http://junon.u-3mrs.fr/monniaux/K84.pdf

In the middle of page 476 of his paper, it's mentioned that "An application of the Hardy-Littlewood inequality thus leads to the inequality...".

I tried to use wiki to find Hardy-Littlewood inequality but I had difficulty applying here. Maybe I got the wrong one. I appreciate if anyone who is familiar with this paper can show me which inequality is the right one to apply here. Thanks!

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  • $\begingroup$ Check the book "Inequalities" by Hardy et. al. $\endgroup$
    – Alan
    Commented Jan 6, 2017 at 18:11

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This is really just a comment, but I don't want to register for the site -- I didn't check the setting in detail, but it is likely that the inequality being referenced here is the Hardy-Littlewood-Sobolev estimate on fractional integrals.

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