  For linear inverse problem with Gaussian random noise we show that Tikhonov
regularization algorithm is minimax in the class of linear estimators and is
asymptotically minimax in the sense of sharp asymptotic in the class of all
estimators. The results are valid if some a priori information on a Fourier
coefficients of solution is provided. For trigonometric basis this a priori
information implies that the solution belongs to a ball in Besov space
$B^r_{2\infty}$.
