Wehrl Inequalities for Matrix Coefficients of Holomorphic Discrete Series
Abstract
Abstract Let G be a Hermitian Lie group. We prove Wehrl-type $$L^2(G)-L^{p}(G)$$ L 2 ( G ) - L p ( G ) inequalities for matrix coefficients of vector-valued holomorphic discrete series of G , for even integers $$p=2n$$ p = 2 n . The optimal constant is expressed in terms of Harish-Chandra formal degrees for the discrete series. We prove the maximizers are precisely the reproducing kernels.
Fields of Study & Subjects
Holomorphic and Operator Theory
Algebraic and Geometric Analysis
Mathematical functions and polynomials
Publication details
- Journal / source
- Journal of Geometric Analysis
- Publisher
- Springer Science and Business Media LLC
- Volume
- 36
- Issue
- 10
- Publication date
- 17 August 2026
- Language
- EN