Bott-Chern harmonic forms and primitive decompositions on compact almost K\"ahler manifolds

Let $(X,J,\omega )$ be a compact $2n$-dimensional almost K"ahler manifold. We prove primitive decompositions for Bott-Chern and Aeppli harmonic forms in special bidegrees and show that such bidegrees are optimal. We also show how the spaces of primitive Bott-Chern, Aeppli, Dolbeault and $\mathrm{\partial }$-harmonic forms on $(X,J,\omega )$ are related.