标题： Rhaly矩阵的有界性、紧性和Schatten类 显示英文标题

标题： Boundedness, compactness and Schatten class for Rhaly matrices

摘要： 本文中我们给出了Rhaly矩阵（也称为阶梯状矩阵）有界性和在$\ell^2$上紧性的新证明。 我们完全刻画了当这些矩阵属于$\mathcal{S}^q(\ell^2)$类时的条件，其中$1<q<\infty$成立。 最后，我们将所得结果应用于加权Dirichlet空间中的Hadamard乘子问题，回答了Mashreghi-Ransford遗留的一个问题。 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.