The Weak Lefschetz Theorem states that for a compact Kahler manifold, $Pic(X) \rightarrow H^{1,1}(X, \mathbb{Z})$ is surjective.

The Hard Lefschetz Theorem states that for a compact Kahler manifold with Lefschetz operator $L$, $$L^{n-k}: H^k(X,\mathbb{R}) \cong H^{2n-k}(X,\mathbb{R})$$ and for any $k$ $$H^k(X, \mathbb{R}) = \bigoplus_{i \geq 0}L^iH^{k-2i}(X, \mathbb{R})_p$$ The subscript $p$ denotes the primitive cohomology groups.

The decomposition above respects the $p,q$ form decomposition of Dolbeault cohomology.

**My question is: what is the relation between these two Lefschetz theorems? Does one imply the other? Any good references?**