Difference between revisions of "Multilinear Airy estimates"

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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>[references.html#CoKeStTaTk-p2 CoKeStTkTa-p2]]
+
* 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: [[references.html#CoKeStTaTk-p2 CoKeStTkTa-p2], [references.html#CoKeStTaTk-p3 CoKeStTkTa-p3]]
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* The analogue for this on '''T''' is: [[Bibliography#CoKeStTaTk-p2 |CoKeStTkTa-p2]], [[Bibliography#CoKeStTaTk-p3 |CoKeStTkTa-p3]]
  
<center><tt><font size="10.0pt">\<span class="SpellE">int</span> u^3 v^2 <span class="SpellE">dx</span> <span class="SpellE">dt</span> <~ || u ||<span class="GramE">_{</span>1/2,1/2*}^3 || v ||_{-1/2,1/2*}^2</font></tt></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:

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