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Timeline for An asymmetric quadrilinear estimate

Current License: CC BY-SA 4.0

7 events
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Apr 1 at 21:31 vote accept Medo
S Mar 30 at 21:18 history edited fedja CC BY-SA 4.0
Only typos
S Mar 30 at 21:18 history suggested Medo CC BY-SA 4.0
Only typos
Mar 30 at 21:15 comment added fedja @Medo Nope to the first: $\beta$ is the denominator size, so it is $1-x^2-y^2$, indeed. Yes to the second: $\alpha$ and $\beta$ are as you said. I was just a bit sloppy in the formula (it was supposed to mean "each of $\alpha$ and $\beta$ is of the kind $2^{-k}$ for possibly different $k$")
Mar 30 at 19:21 comment added Medo Thank you so much for your answer. Many nice and useful tricks here. In the proof of the sufficient condition, did you mean to put $x^2+y^2$ (rather than $1-x^2-y^2$) in the dyadic set of size about $\beta$ ? Also, I can't see why we can set $\alpha,\beta=2^{-k}$, $k\geq 0$. Do you mean $\alpha=2^{-k_{1}}$, $\beta=2^{-k_{2}}$, $k_{1},k_{2}\geq 0$ and then translate the relation between $\alpha $ and $\beta$ into restrictions on the double sum ? Thank you.
Mar 30 at 18:19 review Suggested edits
S Mar 30 at 21:18
Mar 30 at 3:08 history answered fedja CC BY-SA 4.0