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Article Dans Une Revue Mathematical Research Letters Année : 2013

Restriction estimates via the derivatives of the heat semigroup and connection with dispersive estimates

Résumé

We consider an abstract non-negative self-adjoint operator H on an L2- space. We derive a characterization for the restriction estimate lldEH(λ)/dλll Lp→Lp ≤ Cλ d/2 (1/p − 1/p')−1 (involving the Radon-Nikodym derivative of the spectral measure) 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 Lp − Lp' estimates for the derivatives of the spectral resolution of H.
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Dates et versions

hal-00998126 , version 1 (07-07-2017)

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Frederic Bernicot, El Maati Ouhabaz. Restriction estimates via the derivatives of the heat semigroup and connection with dispersive estimates. Mathematical Research Letters, 2013, 20 (6), pp.1047-1058. ⟨10.4310/MRL.2013.v20.n6.a4⟩. ⟨hal-00998126⟩
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