Restriction estimates via the derivatives of the heat semigroup and connection with dispersive estimates
Frédéric Bernicot, El Maati Ouhabaz · Mathematical Research Letters · 2013
We consider an abstract non-negative self-adjoint operator H on an L 2space.We derive a characterization for the restriction estimate-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 L p -L p estimates for the derivatives of the spectral resolution of H.