  In this paper we consider convex Tikhonov regularisation for the solution of
linear operator equations on Hilbert spaces. We show that standard fractional
source conditions can be employed in order to derive convergence rates in terms
of the Bregman distance, assuming some stronger convexity properties of either
the regularisation term or its convex conjugate. In the special case of
quadratic regularisation, we are able to reproduce the whole range of H\"older
type convergence rates known from classical theory.
