Multilinear Airy estimates: Difference between revisions
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* 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>[references.html#CoKeStTaTk-p2 CoKeStTkTa-p2]] | ||
<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]] | * The analogue for this on '''T''' is: [[references.html#CoKeStTaTk-p2 CoKeStTkTa-p2], [references.html#CoKeStTaTk-p3 CoKeStTkTa-p3]] | ||
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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]] | |||
Revision as of 05:11, 28 July 2006
The following multilinear estimates for the Airy equation are known:
- We have the quintilinear estimate on R: [[references.html#CoKeStTaTk-p2 CoKeStTkTa-p2]]
- The analogue for this on T is: [[references.html#CoKeStTaTk-p2 CoKeStTkTa-p2], [references.html#CoKeStTaTk-p3 CoKeStTkTa-p3]]
In fact, this estimate also holds for large period, but a loss of lambda^{0+}.
