Wehrl first investigated Wehrl-type inequalities while studying entropy in quantum mechanics. They can be formulated as inequalities of integrals of matrix coefficients of Lie groups, and the main question is to find states with minimal entropy. In this talk we prove L^2 − L^p Wehrl-type inequalities for the holomorphic discrete series representations of semisimple Lie groups. We find the best constants for inequalities and characterize the maximizers for even integers. This is joint work with Genkai Zhang.
