# 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>: | + | * 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+}.