The authors have retracted this article [1] because of an error in the proof of the first lemma. The gap in the proof has the effect that the main result is incorrect and this affects all other results in the paper. Both authors agree to this retraction. [1] Qi Lü, Jan van Neerven *Conditional expectations in \(L^p(\mu ;L^q(\nu ;X))\) Positivity (2017) DOI 10.1007/s11117-017-0477-x The online version of this article contains the full text of the retracted article as electronic supplementary material.