论文标题
各向异性的总结性和混合序列
An anisotropic summability and mixed sequences
论文作者
论文摘要
在本文中，我们定义和研究一个矢量值序列空间，称为各向异性$（s，q，r）$ - 可总结序列，该序列概括了$（s; q）$ - 混合序列（或混合$（s; q）$ - 可总结序列）的经典空间。此外，我们定义了涉及这个新空间的两类线性运算符，其中一个概括了$（s; q）$的线性运算符的类别A. Pietsch。为这些类别提供了一些特征，包含结果和Pietsch支配型定理。值得一提的是，即使在可混合的总结序列和混合求和操作员混合的情况下，其中一些结果也是新的。
In this paper we define and study a vector-valued sequence space, called the space of anisotropic $(s,q,r)$-summable sequences, that generalizes the classical space of $(s; q)$-mixed sequences (or mixed $(s; q)$-summable sequences). Furthermore, we define two classes of linear operators involving this new space and one of them generalizes the class of $(s; q) $-mixed linear operators due A. Pietsch. Some characterizations, inclusion results and a Pietsch domination-type theorem are presented for these classes. It is worth mentioning that some of these results are new even in the particular cases of mixed summable sequences and mixed summing operators.
