论文标题
Bloch功能和Bekollé-Bonami重量
Bloch functions and Bekollé-Bonami weights
论文作者
论文摘要
我们研究了Bekollé-Bonami重量的情况下，Muckenhoupt重量与$ bmo $之间的众所周知关系的类似物。对于有限双曲线振荡的Bekollé-Bonami重量，我们在设备盘和双曲线Lipschitz功能上提供了Garnett和Jones-type的距离公式。这导致了此类中所有权重的表征，重量的任何功率都是Bekollé-Bonami重量，特别是揭示了Bekollé-Bonami权重和Bloch功能之间的紧密联系。关于表征Bloch空间中有界分析函数的闭合的开放问题，我们为相关最近的猜想提供了反例。这将光明降低了在等于Bloch Norm的近似问题中保持和谐的困难。最后，我们将结果应用于研究Cesaró操作员的某些光谱特性。
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.
