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My question is in reference to this question previously asked here. As asked there, consider a function $f \in H^s_x(L^2_y) \cap L^2_x(H^s_y)$. In the notation of Lions and Magenes (Chapter 4, Vol 2), that means $f \in H^{s,0} \cap H^{0, s}$. My question is, does it follow that $f \in H^{s/2}([0, T], H^{s/2}(\Omega))$? Here $H^{s/2}([0, T], H^{s/2}(\Omega))$ means $H^{s/2}$-valued $H^{s/2}$-functions defined on $[0, T] \subset \mathbb{R}$. This needs some interpolation result, but I cannot find a reference for it.

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