标题： 有界性、紧性和Schatten类对于Rhaly矩阵 显示英文标题

标题： Boundedness, compactness and Schatten class for Rhaly matrices

摘要： 在本文中，我们为Rhaly矩阵（也称为梯田矩阵）在$\ell^2$上的有界性和紧性提供了新的证明。我们完全表征了这些矩阵属于Schatten类$\mathcal{S}^q(\ell^2)$的情况，其中$1<q<\infty$。最后，我们将结果应用于研究加权Dirichlet空间中的Hadamard乘子，回答了Mashreghi-Ransford遗留的问题。 显示英文摘要

摘要： In this article we present new proofs for the boundedness and the compactness on $\ell^2$ of the Rhaly matrices, also known as terraced matrices. We completely characterize when such matrices belong to the Schatten class $\mathcal{S}^q(\ell^2)$, for $1<q<\infty$. Finally, we apply our results to study the Hadamard multipliers in weighted Dirichlet spaces, answering a question left open by Mashreghi-Ransford.