2020/09/22 by Adem Limani, Limani, Adem, Artur Nicolau +1 · 2 citations
Mathematics · #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2009.10445
openalex publication_date 2020/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study analogues of well-known relationships between Muckenhoupt weights and BMO in the setting of Bekollé-Bonami weights. For Bekollé-Bonami weights of bounded hyperbolic oscillation, we provide distance formulas of Garnett and Jones-type, in the context of BMO on the unit disc and hyperbolic Lipschitz functions. This leads to a characterization of all weights in this class, for which any power of the weight is a Bekollé-Bonami weight, which in particular reveals an intimate connection between Bekollé-Bonami weights and Bloch functions. On the open problem of characterizing the closure of bounded analytic functions in the Bloch space, we provide a counter-example to a related recent conjecture. This shed light into the difficulty of preserving harmonicity in approximation problems in norms equivalent to the Bloch norm. Finally, we apply our results to study certain spectral properties of Cesaró operators.