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We revisit the main results from \cites{BGN_SoCG14,BGN_SIAM15} and\cite{LafforgueNaor14_GD} about the impossibility of dimension reduction fordoubling subsets of $\ell_q$ for $q>2$. We provide an alternative elementaryproof of this impossibility result that combines the simplicity of theconstruction in \cites{BGN_SoCG14,BGN_SIAM15} with the generality of theapproach in \cite{LafforgueNaor14_GD} (except for $L_1$ targets). One advantageof this different approach is that it can be naturally generalized to obtainembeddability obstructions into non-positively curved spaces or asymptoticallyuniformly convex Banach spaces.

No dimension reduction for doubling subsets of $\ell_q$ when $q>2$ revisited