  The present work considers one of the simplest homogeneous spaces of the
quantum group SU(1,1), the q-analogue of the unit disc in ${\Bbb C}$. We state
without proofs q-analogues of Cauchy-Green formulae, integral representations
of eigenfunctions of the Laplace-Beltrami operator, Green functions for Poisson
equation and an inversion formula for Fourier transform. It is also
demonstrated that the two-parameter quantization of the disc introduced before
by S. Klimec and A. Lesniewski, can be derived via an application of the method
of F. Berezin.
