Wehrl-Type Inequalities for Bergman Spaces on Domains in C^d and Completely Positive Maps

Paper in proceeding, 2024

We prove certain Wehrl type Lp-inequalities for the Bergman spaces on bounded domains D in Cd and apply the result to bounded symmetric domains D=G/K. We introduce also G-invariant completely positive trace preserving map A→T(A) from operators A on a weighted Bergman space Hμ on D=G/K to operators T(A) on another weighted Bergman space Hμ+ν and prove that the Lp-norm of Bergman functions f∈Hμ can be obtained as limit of trace of T(f⊗f∗) as the weight ν→∞.