In this note we estimate the asymptotic rates for the L-2-error decay and the storage cost when approximating 2 pi-periodic, d-variate functions from isotropic and mixed Sobolev classes by the recent hierarchical tensor format as introduced by Hackbusch and Kuhn. To this end, we survey some results on bilinear approximation due to Temlyakov. The approach taken in this paper improves and generalizes recent results of Griebel and Harbrecht for the bi-variate case. (C) 2013 Elsevier Inc. All rights reserved.