Best m-term aproximation and tensor product of Sobolev and Besov spaces-the case of non-compact embeddings

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Efficient Analysis of High Dimensional Data in Tensor Formats (2012, background): “Let us take a finite element ansatz UN := {φn(x)}n=1 ⊂ U [34, 6, 39] as a corresponding subspace, such that the solution may be approximated by:”
Hyperbolic Cross Approximation (2016, methodology): “The bound is a simple consequence of recent results [166, 168] on best m-term approximation for non-compact embeddings Wr p ↪→ Lq if 1 < p < q < ∞ and r = 1/p− 1/q, and Bp,p ↪→ Lq if 0 < p ≤ max{p, 1} < q < ∞ and r = 1/p − 1/q, see Theorems 9.”