  Learning rates for least-squares regression are typically expressed in terms
of $L_2$-norms. In this paper we extend these rates to norms stronger than the
$L_2$-norm without requiring the regression function to be contained in the
hypothesis space. In the special case of Sobolev reproducing kernel Hilbert
spaces used as hypotheses spaces, these stronger norms coincide with fractional
Sobolev norms between the used Sobolev space and $L_2$. As a consequence, not
only the target function but also some of its derivatives can be estimated
without changing the algorithm. From a technical point of view, we combine the
well-known integral operator techniques with an embedding property, which so
far has only been used in combination with empirical process arguments. This
combination results in new finite sample bounds with respect to the stronger
norms. From these finite sample bounds our rates easily follow. Finally, we
prove the asymptotic optimality of our results in many cases.
