Optimal convergence rates for Tikhonov regularization in Besov scales

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 vice versa. Moreover, we present optimal source conditions for regularization in Besov scales.