  This paper deals with Tikhonov regularization for linear and nonlinear
ill-posed operator equations with wavelet Besov norm penalties. We show order
optimal rates of convergence for finitely smoothing operators and for the
backwards heat equation for a range of Besov spaces using variational source
conditions. We also derive order optimal rates for a white noise model with the
help of variational source conditions and concentration inequalities for sharp
negative Besov norms of the noise.
