New characterization of plurisubharmonic functions and positivity of direct image sheaves

We discover a new characterization of plurisubharmonic functions in terms of Lᵖ extension from one point and Griffiths positivity of holomorphic vector bundles with singular Finsler metrics in terms of Lᵖ extensions. As applications, we give a stronger result or new proof of some well-known theorems on the Griffiths positivity of the holomorphic vector bundles and their direct image sheaves associated to certain holomorphic fibrations.