一类矩阵算子范数的双面估计

Siberian Advances in Mathematics Pub Date : 2022-03-17 DOI:10.1134/s1055134422010035

A. A. Kalybay

引用次数: 0

摘要

摘要:对于$ 1<p,q<\infty $，我们得到了一个离散hardy型不等式$$ \left (\sum \limits_{n=1}^{\infty }|(Af)_n|^q\right )^{\frac {1}{q}} \le C\left (\sum \limits_{k=1}^{\infty }|f_k|^p\right )^{\frac {1}{p}}$$的充要条件，这类矩阵算子形式为$(Af)_n=\sum \limits _{k=1}^{n}a_{n,k}f_k $，其中$n\ge 1 $。

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Two-Sided Estimates of the Norm for a Class of Matrix Operators

Abstract

For $ 1<p,q<\infty $, we find necessary and sufficient conditions for the validity of a discrete Hardy-type inequality

$$ \left (\sum \limits _{n=1}^{\infty }|(Af)_n|^q\right )^{\frac {1}{q}} \le C\left (\sum \limits _{k=1}^{\infty }|f_k|^p\right )^{\frac {1}{p}}$$

for a class of matrix operators of the form $(Af)_n=\sum \limits _{k=1}^{n}a_{n,k}f_k $, where $n\ge 1 $.

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来源期刊

Siberian Advances in Mathematics Mathematics-Mathematics (all)

CiteScore

0.70

自引率

0.00%

发文量

期刊介绍： Siberian Advances in Mathematics is a journal that publishes articles on fundamental and applied mathematics. It covers a broad spectrum of subjects: algebra and logic, real and complex analysis, functional analysis, differential equations, mathematical physics, geometry and topology, probability and mathematical statistics, mathematical cybernetics, mathematical economics, mathematical problems of geophysics and tomography, numerical methods, and optimization theory.