论文标题
贝尔曼的功能对哈迪对二元树的不平等
Bellman function for Hardy's inequality over dyadic trees
论文作者
论文摘要
在本文中，我们使用Bellman功能技术来表征加权Hardy不平等对二元树的措施。我们阐明了（双重）Hardy在二元树上的不平等，并使用相关的“ Burkholder-type”功能来找到结果证明所需的主要不平等。我们阐明满足所需属性的“钟声型”函数，并使用Bellman功能技术来证明本文的主要结果。我们证明了相关常数的最佳性，其明确的地图家族的明确例子。我们还根据随机最佳控制理论对相应的Bellman功能进行了明确的解释。
In this article we use the Bellman function technique to characterize the measures for which the weighted Hardy's inequality holds on dyadic trees. We enunciate the (dual) Hardy's inequality over the dyadic tree and we use the associated "Burkholder-type" function to find the main inequality required in the proof of the result. We enunciate a "Bellman-type" function satisfying the required properties and we use the Bellman function technique to prove the main result of this article. We prove the optimality of the associated constant with an explicit example of an extremal family of maps. We also give an explicit interpretation of the corresponding Bellman function in terms of the theory of stochastic optimal control.
