Stability of Wehrl-type Functionals and Concentration Estimates on Bergman Spaces of Log-Subharmonic Functions on the Unit Sphere

2025/12/17 by Jaguzović, Vladan, Melentijević, Petar
Mathematics · #Holomorphic and Operator Theory #Geometry and complex manifolds #Algebraic and Geometric Analysis

paper · doi:10.48550/arxiv.2512.15193

Abstract

In this paper, we consider weighted Bergman spaces B_α,p of log-subharmonic functions on the unit sphere. Using the isoperimetric inequality for the spherical metric we prove certain monotonicity property for super-level sets of |f(x)|^pW_n^α(x), where f∈ B_α,p and W_n^α(x) is the Bergman weight. As a consequence, we solve a maximization problem for certain Wehrl-type (convex) functionals and concentration estimates. Moreover, we show the stability of these estimates, proving that near-extremizing values are achieved for near-extremizing functions.

Citations

• Sharp stability of convex functionals on weighted Bergman spaces with applications
• The Wehrl-type entropy conjecture for symmetric SU(N) coherent states: cases of equality and stability
• Uniform stability of concentration inequalities and applications
• Stability of the concentration inequality on polynomials
• The generalized Wehrl entropy bound in quantitative form
• Stability of the Faber-Krahn inequality for the Short-time Fourier Transform
• A Faber-Krahn type inequality for log-subharmonic functions in the hyperbolic ball
• A monotonicity theorem for subharmonic functions on manifolds
• Sharp inequalities for coherent states and their optimizers
• A Faber-Krahn inequality for wavelet transforms
• Functionals with extrema at reproducing kernels

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