Hardy-type inequalities for matrix operators
We establish necessary and sufficient conditions the validity of the discrete Hardy - type inequality (∑∞i=1(∑∞j=1ai,jfj)quiq)1/q ≤ (∑∞i=1 fipvip)1/p, f={fi}∞i=1≥0, with 0 < p ≤ q < ∞ and 0 < p ≤ 1, where the matrices (ai;j) is an arbitrary matrix and the entries of the matrix (ai;j) ≥ 0 s...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2017-12-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Subjects: | |
| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/186 |
| Summary: | We establish necessary and sufficient conditions the validity of the discrete Hardy - type inequality (∑∞i=1(∑∞j=1ai,jfj)quiq)1/q ≤ (∑∞i=1 fipvip)1/p, f={fi}∞i=1≥0, with 0 < p ≤ q < ∞ and 0 < p ≤ 1, where the matrices (ai;j) is an arbitrary matrix and the entries of the matrix (ai;j) ≥ 0 such that ai;j is non - increasing in the second index. Also some further results are pointed out on the cone of monotone sequences. Moreover, we give that the applications of the main results for the non - negative and triangular matrices (ai;j ≥ 0 for 1 ≤ j ≤ i and ai;j = 0 for i < j).
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| ISSN: | 2518-7929 2663-5011 |