论文标题
对广义stieltjes的理论转变
To the theory of generalized Stieltjes transforms
论文作者
论文摘要
我们确定在广义stieltjes变换的产物中产生的措施，作为广义stieltjes变换，为这些度量的大小提供了最佳估计，并解决了广义的Cauchy Transforms的类似问题。在后一种情况下，在两种特定设置中，我们提供标准，以确保措施是积极的。以此方式，我们还获得了新的，适用的条件，以代表函数作为广义的stieltjes变换，从而为Sokal提出的问题提供了部分答案，并在最近在概率研究中出现了光谱乘数。作为我们方法的副产品，我们在Stieltjes和Hilbert Transforms上提高了几个已知结果。
We identify measures arising in the representations of products of generalized Stieltjes transforms as generalized Stieltjes transforms, provide optimal estimates for the size of those measures, and address a similar issue for generalized Cauchy transforms. In the latter case, in two particular settings, we give criteria ensuring that the measures are positive. On this way, we also obtain new, applicable conditions for representability of functions as generalized Stieltjes transforms, thus providing a partial answer to a problem posed by Sokal and shedding a light at spectral multipliers emerged recently in probabilistic studies. As a byproduct of our approach, we improve several known results on Stieltjes and Hilbert transforms.
