Multilinear Airy estimates: Difference between revisions

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The following multilinear estimates for the [[Airy equation]] are known:
The following multilinear estimates for the [[Airy equation]] are known:


* We have the <span class="SpellE">quintilinear</span> estimate on '''R'''<nowiki>: </nowiki>[[Bibliography#CoKeStTaTk-p2 |CoKeStTkTa-p2]]
* We have the <span class="SpellE">quintilinear</span> estimate on '''R'''<nowiki>: </nowiki>[[CoKeStTkTa2003]]


<center><math>\int u^3 v^2 dt <~ || u ||_{1/4+,1/2+}^3 || v ||_{-3/4+,1/2+}^2</math></center>
<center><math>\int u^3 v^2 dt <~ || u ||_{1/4+,1/2+}^3 || v ||_{-3/4+,1/2+}^2</math></center>


* The analogue for this on '''T''' is: [[Bibliography#CoKeStTaTk-p2 |CoKeStTkTa-p2]], [[Bibliography#CoKeStTaTk-p3 |CoKeStTkTa-p3]]
* The analogue for this on '''T''' is: [[CoKeStTkTa2003]], [[CoKeStTkTa-p3]]


<center><math>
<center><math>

Latest revision as of 22:48, 14 August 2006

The following multilinear estimates for the Airy equation are known:

In fact, this estimate also holds for large period, but a loss of lambda^{0+}.