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

Frederic Bernicot, El Maati Ouhabaz

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(λ) \|_{L^p \to L^{p'}} \le C λ^…