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>: | * We have the <span class="SpellE">quintilinear</span> estimate on '''R'''<nowiki>: </nowiki>[[Bibliography#CoKeStTaTk-p2 |CoKeStTkTa-p2]] | ||
<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: [[ | * The analogue for this on '''T''' is: [[Bibliography#CoKeStTaTk-p2 |CoKeStTkTa-p2]], [[Bibliography#CoKeStTaTk-p3 |CoKeStTkTa-p3]] | ||
<center>< | <center><math> | ||
int u^3 v^2 dxdt <~ | |||
|| u ||_{1/2,1/2*}^3 || v ||_{-1/2,1/2*}^2 | |||
</math></center> | |||
In fact, this estimate also holds for large period, but a loss of lambda<span class="GramE">^{</span>0+}. | In fact, this estimate also holds for large period, but a loss of lambda<span class="GramE">^{</span>0+}. | ||
[[Category:Estimates]] | [[Category:Estimates]] | ||
Revision as of 16:34, 31 July 2006
The following multilinear estimates for the Airy equation are known:
- We have the quintilinear estimate on R: CoKeStTkTa-p2
- The analogue for this on T is: CoKeStTkTa-p2, CoKeStTkTa-p3
In fact, this estimate also holds for large period, but a loss of lambda^{0+}.
