  It is well-known that the problem of sampling recovery in the $L_2$-norm on
unweighted Korobov spaces (Sobolev spaces with mixed smoothness) as well as
classical smoothness classes such as H\"older classes suffers from the curse of
dimensionality. We show that the problem is tractable for those classes if they
are intersected with the Wiener algebra of functions with summable Fourier
coefficients. In fact, this is a relatively simple implication of powerful
results from the theory of compressed sensing. Tractability is achieved by the
use of non-linear algorithms, while linear algorithms cannot do the job.
