  The aim of this paper is to obtain a generalized CK-extension theorem in
superspace for the bi-axial Dirac operator. In the classical commuting case,
this result can be written as a power series of Bessel type of certain
differential operators acting on a single initial function. In the superspace
setting, novel structures appear in the cases of negative even superdimensions.
In these cases, the CK-extension depends on two initial functions on which two
power series of differential operators act. These series are not only of Bessel
type but they give rise to an additional structure in terms of Appell
polynomials. This pattern also is present in the structure of the Pizzetti
formula, which describes integration over the supersphere in terms of
differential operators. We make this relation explicit by studying the
decomposition of the generalized CK-extension into plane waves integrated over
the supersphere. Moreover, these results are applied to obtain a decomposition
of the Cauchy kernel in superspace into monogenic plane waves, which shall be
useful for inverting the super Radon transform.
