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- W2274434041 abstract "This note establishes the full range of $L^p$--$L^q$ Fourier extension estimates for the model $n$-dimensional quadratic submanifold in ${mathbb R}^{n(n+3)/2}$ parametrized by $gamma(x_1,ldots,x_n) := (x_1,ldots,x_n, (x_i x_j)_{1 leq i leq j leq n})$. This class of submanifolds is extremal in the sense that an $n$-dimensional quadratic submanifold of ${mathbb R}^d$ can only satisfy nontrivial Fourier extension inequalities when $d leq frac{n(n+3)}{2}$. The proof is via an inflation-type argument, with the unexpected twist that a significant amount of overinflation is necessary but in no way limits the sharpness of the argument." @default.
- W2274434041 created "2016-06-24" @default.
- W2274434041 creator A5073463363 @default.
- W2274434041 date "2016-02-15" @default.
- W2274434041 modified "2023-09-27" @default.
- W2274434041 title "Fourier extension for extremal quadratic submanifolds" @default.
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