  We consider the problem of estimating a density $f_X$ using a sample
$Y_1,...,Y_n$ from $f_Y=f_X\star f_{\epsilon}$, where $f_{\epsilon}$ is an
unknown density. We assume that an additional sample
$\epsilon_1,...,\epsilon_m$ from $f_{\epsilon}$ is observed. Estimators of
$f_X$ and its derivatives are constructed by using nonparametric estimators of
$f_Y$ and $f_{\epsilon}$ and by applying a spectral cut-off in the Fourier
domain. We derive the rate of convergence of the estimators in case of a known
and unknown error density $f_{\epsilon}$, where it is assumed that $f_X$
satisfies a polynomial, logarithmic or general source condition. It is shown
that the proposed estimators are asymptotically optimal in a minimax sense in
the models with known or unknown error density, if the density $f_X$ belongs to
a Sobolev space $H_{\mathbh p}$ and $f_{\epsilon}$ is ordinary smooth or
supersmooth.
