标题： 稀疏集的高函数：贝尔曼函数方法 显示英文标题

标题： The height function of a sparse collection: a Bellman function approach

摘要： 稀疏算子已成为在调和分析不等式中提取精确常数的强大方法，例如在有界奇异积分算子的上下文中。 我们研究稀疏集合的高度函数的水平集，或者换句话说，稀疏算子作用于常数函数时的弱型(1,1)不等式。 我们使用来自二进制调和分析的另一种著名方法，该方法也以其生成精确常数的能力而闻名，即贝尔曼函数方法。 具体而言，我们找到最大化$\mathcal{A}_\alpha 1\!\!1$水平集的精确贝尔曼函数，其中 $\mathcal{A}_\alpha$是与二进制Carleson序列相关的（局部化）稀疏算子。 显示英文摘要

摘要： Sparse operators have emerged as a powerful method to extract sharp constants in harmonic analysis inequalities, for example in the context of bounding singular integral operators. We investigate the level sets of height functions for sparse collections, or, in other words, weak-type (1,1) inequalities for sparse operators applied to constant functions. We use another notable method from dyadic harmonic analysis, also famous for its ability to produce sharp constants, the Bellman function method. Specifically, we find the exact Bellman function maximizing level sets of $\mathcal{A}_\alpha 1\!\!1$, where $\mathcal{A}_\alpha$ is the (localized) sparse operator associated with a binary Carleson sequence.