In the proof of Lemma 4.1, pp. 962–963 in "Endpoint Strichartz Estimates" by Tao and Keel (1997) (see [MR1646048](https://mathscinet.ams.org/mathscinet-getitem?mr=1646048) or [Zbl 0922.35028](https://zbmath.org/0922.35028)), the authors first proved the statements hold for some boundary and vertex values of $(a,b)$, and then it was claimed that the statements of the Lemma hold true for points in some neighborhood of $(r,r)$ since $(r,r)$ is in the convex hull determined by those boundary and vertex values of $(a,b)$. This is due to interpolation for bilinear forms, according to the expression in the article.

**Question**. I wonder what is interpolation for bilinear forms and how it is used here. Is there some books including this? I merely heard of interpolation for operators between function spaces, and interpolation for functionals of single variable as well. But never saw interpolation for bilinear forms before...

![The lemma in question, and its proof, is shown in this screenshot][1]

  [1]: https://i.sstatic.net/VvXJA.png