  In this paper we deal with linear inverse problems and convergence rates for
Tikhonov regularization. We consider regularization in a scale of Banach
spaces, namely the scale of Besov spaces. We show that regularization in Banach
scales differs from regularization in Hilbert scales in the sense that it is
possible that stronger source conditions may lead to weaker convergence rates
and vive versa. Moreover, we present optimal source conditions for
regularization in Besov scales.
