  In this short note we consider several widely used L^2-orthogonal Helmholtz
decompositions for bounded domains in R^3. It is well known that one part of
the decompositions is a subspace of the space of functions with zero mean. We
refine this global property into a local equivalent: we show that functions
from these spaces have zero mean in every part of specific decompositions of
the domain.
  An application of the zero mean properties is presented for convex domains.
We introduce a specialized Poincare-type inequality, and estimate the related
unknown constant from above. The upper bound is derived using the upper bound
for the Poincare constant proven by Payne and Weinberger. This is then used to
obtain a small improvement of upper bounds of two Maxwell-type constants
originally proven by Pauly.
  Although the two dimensional case is not considered, all derived results can
be repeated in R^2 by similar calculations.
