We discuss the Wehrl-type entropy inequality conjecture for the group SU(1,1) and for its subgroup AX+B (or affine group), their representations on L2(R+), and their coherent states. For AX+B the Wehrl-type conjecture for Lp-norms of these coherent states (also known as the Renyi entropies) is proved in the case that p is an even integer. We also show how the general AX+B case reduces to an unsolved problem about analytic functions on the upper half-plane and the unit disk.

Keywords: Coherent states, affine group, AX+B group