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We know that there exist wavelets generating orthonormal bases in Sobolev spaces $W^{p,s}(\mathbb R^n)$, where $p$ is the index of integral and $s$ is the index of smoothness. Consider the orthonormal system $\{\Psi^{j,G}_m\}$ in Triebel, Theory of Function Spaces III, which are tensor products. Are they also an orthonormal basis in $W^{p,s}$? Moreover, do we have the following equivalence? $$ \|f\|_{W^{p,s}}\approx \Big\|\big( \sum_{j\geq 1,G,m} 2^{2j s} |\langle f, \Psi^{j,G}_m\rangle \Psi^{j,G}_m|^2\big)^{1/2} \Big\|_{L^p}. $$

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