Bergman Projections, Kernel p-Norm Estimates, and Toeplitz Operators with Békollé and Bonami weights

2025/12/10 by Hicham Arroussi, Taskinen, Jari, Arroussi, Hicham +3
Mathematics · #Holomorphic and Operator Theory #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis

paper · pdf · doi:10.48550/arxiv.2512.09885

Abstract

In this paper, we establish entirely new p-norm estimates for reproducing kernels to characterize the bounded and compact Toeplitz operators T_μ acting between weighted Békollé--Bonami Bergman spaces A^p_u(\mathbbD) and A^q_u(\mathbbD) for all positive exponents 0 < p, q < ∞. These operator-theoretic properties are completely described in terms of generalized Berezin transforms, averaging functions, and Carleson measures. We introduce two explicit conditions on the weights to ensure the boundedness of the weighted Bergman projection P_u, generalizing results from Hilbert spaces to Banach spaces.Our work generalizes the main results of Tong, Li, and Arroussi \citeTLA from Hilbert spaces to the more general setting of Banach spaces.

Citations

• Bergman projection on Lebesgue space induced by doubling weight
• Hankel operators induced by radial Bekollé-Bonami weights on Bergman spaces
• Two weight inequality for Bergman projection
• Reproducing kernel estimates, bounded projections and duality on large\n weighted Bergman spaces
• Sharp Bekolle estimates for the Bergman projection
• Toeplitz Operators on Weighted Bergman Spaces

Related

• Toeplitz Operators on Weighted Bergman Spaces
• Berezin transform and Toeplitz operators on weighted Bergman spaces induced by regular weights
• Toeplitz Operators and Berezin-type Operators on Different Bergman Spaces
• The Berezin Transform on the Toeplitz Algebra
• Compact Operators on Vector-Valued Bergman Space via the Berezin\n Transform