Affine Coordinate Subspaces and Strong Khintchine Convergence

We prove that every affine coordinate subspace of positive dimension and positive codimension fails to be of strong Khintchine type for convergence. Combining this with Huang’s criterion for Khintchine-type affine subspaces gives a sufficient Diophantine condition for an affine coordinate subspace to be of Khintchine type but not of strong Khintchine type for convergence.