Bott–Chern harmonic forms and primitive decompositions on compact almost Kähler manifolds

Let (X, J, ?) be a compact 2n-dimensional almost Kahler 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 ?-harmonic forms on (X, J, ?) are related.