Conformally compactified Minkowski superspaces revisited

Starting from the standard supertwistor realizations for conformally compactified N-extended Minkowski superspaces in three and four space-time dimensions, we elaborate on alternative realizations in terms of graded two-forms on the dual supertwistor spaces. The construction is further generalized to the cases of 4D N = 2 and 3D N-extended harmonic/projective superspaces. We present a superconformal Fourier expansion of tensor superfields on the 4D N = 2 harmonic/projective superspace.