Multilinear Airy estimates

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The following multilinear estimates for the Airy equation are known:

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

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

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