Let $(X,g)$ be a Hermitian complex manifold, and let $p,q\ge 0$. Let $\alpha,\beta\in A^{p,q}(X)$ be smooth complex-valued differential forms satisfying
Equip complex-valued differential forms with the $L^2$ Hermitian [inner product](/page/Inner%20Product) induced by $g$, with the convention that it is linear in the first argument and conjugate-linear in the second. Then complex conjugation sends $\alpha$ and $\beta$ to $L^2$ forms