  The relative Dolbeault cohomology which naturally comes up in the theory of
Cech-Dolbeault cohomology turns out to be canonically isomorphic with the local
(relative) cohomology of A. Grothendieck and M. Sato so that it provides a
handy way of representing the latter. In this paper we use this cohomology to
give simple explicit expressions of Sato hyperfunctions, some fundamental
operations on them and related local duality theorems. This approach also
yields a new insight into the theory of hyperfunctions and leads to a number of
further results and applications. As one of such, we give an explicit embedding
morphism of Schwartz distributions into the space of hyperfunctions.
