论文标题
Bakry Riesz Vector的连续稀疏支配和无量纲的加权估计值
Continuous sparse domination and dimensionless weighted estimates for the Bakry Riesz vector
论文作者
论文摘要
我们提供了带有有界几何形状的歧管上Bakry Riesz向量的无量纲LP界限的根本新证明。我们的证明具有显着的优势，即与以前的论点相比，它可以得出更强大的结论，即具有最佳指数的一些新的无量纲加权估计。这项任务的重要性的一部分在于技术的新颖性：我们在统一整合的Cadlag Hilbert Space Reate Martingales中发展了自我相似参数，称为稀疏统治，并将其扩展到无限记忆的过程中。我们为这些随机过程提供了一系列最佳加权估计和弱类型估计。先前的几何riesz变换估计值依赖于Bellman功能，并且没有提供此范围的加权估计。在这种概率环境中稀疏统治的发展及其在高维问题中的使用是新的。
We present a fundamentally new proof of the dimensionless Lp boundedness of the Bakry Riesz vector on manifolds with bounded geometry. Our proof has the significant advantage that it allows for a much stronger conclusion than previous arguments, namely that of some new dimensionless weighted estimates with optimal exponent. Part of the importance of this task lies in the novelty of the techniques: we develop the self similarity argument known as sparse domination in the setting of uniformly integrable cadlag Hilbert space valued martingales and extend the domination to a process with infinite memory. We provide a range of optimal weighted estimates and weak type estimates for these stochastic processes. Previous geometric Riesz transform estimates relied on Bellman functions and did not provide this range of weighted estimates. The development of sparse domination in this probabilistic setting and its use for high dimensional problems is new.
