$$W^{1,2}$$ Bott-Chern and Dolbeault Decompositions on Kähler Manifolds

Let (M, J, g, omega) be a Kahler manifold. We prove a W-1,W-2 weak Bott-Chern decom-position and a W-1,W-2 weak Dolbeault decomposition of the space of W-1,W-2 differential (p, q)-forms, following the L-2 weak Kodaira decomposition on Riemannian man-ifolds. Moreover, if the Kahler metric is complete and the sectional curvature is bounded, the W-1,W-2 Bott-Chern decomposition is strictly related to the space of W-1,W-2 Bott-Chern harmonic forms, i.e., W-1,W-2 smooth differential forms which are in the kernel of an elliptic differential operator of order 4, called Bott-Chern Laplacian.