The main result is a pointwise a-priori estimate for the
-Neumann
problem that holds on an
arbitrary weakly pseudoconvex domain
. It is shown
that for
-forms
in the domain
of the adjoint
of
,
the pointwise growth of the derivatives of each coefficient of
with
respect to
and in complex tangential directions is carefully controlled by the sum of the suprema of
,
, and
over
.
These estimates provide a pointwise analog of the classical basic estimate in the
theory that has been the starting point for all major work in this area involving
and
Sobolev norm estimates for the complex Neumann and related operators.
Keywords
a-priori estimates, $\bar\partial$ Neumann problem,
integral representations, weakly pseudoconvex domains
