  We consider the geodesic X-ray transform acting on solenoidal tensor fields
on a compact simply connected manifold with strictly convex boundary and
non-positive curvature. We establish a stability estimate of the form
$L^2\mapsto H^{1/2}_{T}$, where the $H^{1/2}_{T}$-space is defined using the
natural parametrization of geodesics as initial boundary points and incoming
directions (fan-beam geometry); only tangential derivatives at the boundary are
used. The proof is based on the Pestov identity with boundary term localized in
frequency.
