Bloch Functions and Bekollé-Bonami Weights

Abstract

We study some 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, distance formulas of Garnett and Jones type in the context of BMO on the unit disc and hyperbolic Lipschitz functions are obtained. We provide a counterexample to a recent conjecture, which suggests a certain weight condition for characterizing the closure of bounded analytic functions in the Bloch space. Finally, we include some applications to the spectrum of Cesaró operators on the Bergman spaces. © Indiana University Mathematics Journal.