Restriction estimates via the derivatives of the heat semigroup and connexion with dispersive estimates
Language
en
Article de revue
This item was published in
Mathematical Research Letters. 2013, vol. 20, n° 6, p. 1047-1058
International Press
English Abstract
We consider an abstract non-negative self-adjoint operator $H$ on an $L^2$-space. We derive a characterization for the restriction estimate $\| dE_H(\lambda) \|_{L^p \to L^{p'}} \le C \lambda^{\frac{d}{2}(\frac{1}{p} - ...Read more >
We consider an abstract non-negative self-adjoint operator $H$ on an $L^2$-space. We derive a characterization for the restriction estimate $\| dE_H(\lambda) \|_{L^p \to L^{p'}} \le C \lambda^{\frac{d}{2}(\frac{1}{p} - \frac{1}{p'}) -1}$ in terms of higher order derivatives of the semigroup $e^{-tH}$. We provide an alternative proof of a result in [1] which asserts that dispersive estimates imply restriction estimates. We also prove $L^p-L^{p'}$ estimates for the derivatives of the spectral resolution of $H$.Read less <
Keywords
Restriction estimates
semigroup
spectral multipliers
dispersive estimates
ANR Project
Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013
Origin
Hal imported