“…After Lemmas and , the proof of Theorems and boils down to approximating sharp cut‐offs by smooth kernels and estimating S‐HC transforms. Following , with a hyperbolic version of a classical Euclidean device, it is possible to reduce the problem to estimate the S‐HC transform of the characteristic function of an interval (which is done in [, Lemma 2.4]). With this idea in mind, we write and , respectively, for the characteristic function of and its S‐HC transform: The slow decay of would cause serious convergence problems when applying the spectral theorem.…”