Various Proofs for Hodge Decomposition Theorem

Question

This is the version I am referring it to: $H^{k}_{DR}(X,\mathbb{C})=\bigoplus _{p+q=k}H^{p,q}_{DR}(X)$,where X is a Kahler manifold and $H^{k}_{DR}(X,\mathbb{C})=\dfrac{closed~forms}{exact~forms}$ in $\Omega^{k}(X)$. This a very deep theorem and proofs for it are not readily available (ex. Wikipedia) like for other theorems. So this can be at least one place where we can find various proofs for it.

Answer 1

Here is one: http://dspace.library.uu.nl/handle/1874/283345

The Hodge Decomposition Theorem on Compact Kahler Manifolds