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Two-sided estimates of norms of a class of matrix operators
A. A. Kalybay Kazakhstan Institute of Management, Economics and Strategic Research, Almaty
Abstract:
In the article, we establish 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 one class of matrix operators $$(Af)_n=\sum\limits_{k=1}^{n}a_{n,k}f_k, n\ge 1,$$ for $1<p,q<\infty$.
Key words:
Hardy type inequality, discrete operator, matrix operator, space of sequences.
Received: 23.10.2020 Revised: 12.03.2021 Accepted: 31.03.2021
Citation:
A. A. Kalybay, “Two-sided estimates of norms of a class of matrix operators”, Mat. Tr., 24:2 (2021), 37–45
Linking options:
https://www.mathnet.ru/eng/mt649 https://www.mathnet.ru/eng/mt/v24/i2/p37
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Statistics & downloads: |
Abstract page: | 161 | Full-text PDF : | 37 | References: | 50 | First page: | 1 |
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