关键词: Normality, entire function

Abstract:

A weighted Koppelman-Leray-Norguet formula of $(r,s)$
differential forms on a local $q$-concave wedge  in a complex
manifold is obtained. By constructing the new weighted kernels,
the authors give a new weighted Koppelman-Leray-Norguet formula
without boundary integral of $(r,s)$ differential forms,
which is different from the  classical one.
The new weighted formula is especially suitable for the case
of the local $q$-concave wedge with a non-smooth boundary, so
one can  avoid complex  estimates of  boundary
integrals and the density of integral may be not defined on the
boundary but only in the domain.
Moreover, the weighted integral formulas have much freedom
in applications such as in the interpolation of functions.

Key words: Normality, entire function