Sheaf of vector-bundle-valued differential forms
= Sheaf of vector-bundle-valued differential forms
{title2=$\mathcal A^{p,q}(E)$}
For a <holomorphic vector bundle> $E$, this <sheaf> assigns to $U$ the smooth $E$-valued <differential forms of type (p, q)> on $U$. Its <Dolbeault operator> acts coefficientwise in a <holomorphic local frame> and squares to zero.