  Aim of this article is a Satake type theorem for super automorphic forms on a
complex bounded symmetric super domain B of rank 1 with respect to a lattice.
This theorem - roughly speaking - says that for large weight k and all p from 1
to infinity (both including) a super automorphic form on B is a super cusp form
if and only if its p-norm with respect to a certain measure on the quotient of
B is finite. And so in particular all these Lp-spaces coincide! We will give a
proof of this theorem using an unbounded realization of B and Fourier
decomposition at the cusps of the quotient mapped to infinity via a partial
Cayley transform.
