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Apr 16, 2021 at 5:20 answer added Martin Väth timeline score: 3
Apr 16, 2021 at 4:45 history edited Daniele Tampieri CC BY-SA 4.0
(Very) minor formatting.
Apr 16, 2021 at 3:00 comment added Willie Wong By the way, I think you should be asking about interpolation spaces and not just the intersection space. There are a lot of spaces that contain $L^\phi \cap L^\psi$. The interpolation spaces have the property that the norm can be bounded by something like $\|u\|_{L^\phi}^\theta \|u\|_{L^\psi}^{1-\theta}$. In that vein, Googling finds me eudml.org/doc/218150
Apr 16, 2021 at 2:50 comment added Willie Wong Well, $u^r \leq \max( u^p, u^q)$ for every $u\in [0,\infty)$, and this gives another proof that $L^p\cap L^q \subset L^r$. So the obvious modification using Young's functions should still work.
Apr 16, 2021 at 0:16 history edited Guy Fsone CC BY-SA 4.0
added 12 characters in body
Apr 16, 2021 at 0:11 history asked Guy Fsone CC BY-SA 4.0