| Title:
|
Lower bound and upper bound of operators on block weighted sequence spaces (English) |
| Author:
|
Lashkaripour, Rahmatollah |
| Author:
|
Talebi, Gholomraza |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
293-304 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $A=(a_{n,k})_{n,k\geq 1}$ be a non-negative matrix. Denote by $L_{v,p,q,F}(A)$ the supremum of those $L$ that satisfy the inequality $$ \|Ax\|_{v,q,F} \ge L\| x\|_{v,p,F}, $$ where $x\geq 0$ and $x\in l_p(v,F)$ and also $v=(v_n)_{n=1}^\infty $ is an increasing, non-negative sequence of real numbers. If $p=q$, we use $L_{v,p,F}(A)$ instead of $L_{v,p,p,F}(A)$. In this paper we obtain a Hardy type formula for $L_{v,p,q,F}(H_\mu )$, where $H_\mu $ is a Hausdorff matrix and $0<q\leq p\leq 1$. Another purpose of this paper is to establish a lower bound for $\|A_{W}^{NM} \|_{v,p,F}$, where $A_{W}^{NM}$ is the Nörlund matrix associated with the sequence $W=\{w_n\}_{n=1}^\infty $ and $1<p<\infty $. Our results generalize some works of Bennett, Jameson and present authors. (English) |
| Keyword:
|
lower bound |
| Keyword:
|
weighted sequence space |
| Keyword:
|
Hausdorff matrices |
| Keyword:
|
Euler matrices |
| Keyword:
|
Cesàro matrices |
| Keyword:
|
Hölder matrices |
| Keyword:
|
Gamma matrices |
| MSC:
|
26D15 |
| MSC:
|
40G05 |
| MSC:
|
46A45 |
| MSC:
|
47A30 |
| MSC:
|
54D55 |
| idZBL:
|
Zbl 1265.26074 |
| idMR:
|
MR2990178 |
| DOI:
|
10.1007/s10587-012-0031-8 |
| . |
| Date available:
|
2012-06-08T09:34:20Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142829 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
[7] Foroutannia, D.: Upper bound and lower bound for matrix operators on weighted sequence space.PhD. Thesis Zahedan (2007). |
| Reference:
|
[8] Jameson, G. J. O., Lashkaripour, R.: Norms of certain operators on weighted $l_p$ spaces and Lorentz sequence spaces.JIPAM, J. Inequal. Pure Appl. Math. 3 (2002), Electronic only. Zbl 1021.47019, MR 1888921 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[11] Lashkaripour, R., Foroutannia, D.: Computation of matrix operators bounds with applying new extension of Hardy inequality on weighted sequence spaces. I.Lobachevskii J. Math. 30 (2009), 40-45. Zbl 1177.26039, MR 2506053, 10.1134/S1995080209010065 |
| Reference:
|
[12] Lashkaripour, R., Talebi, G.: Lower bound of Copson type for Hausdorff matrices on weighted sequence spaces.J. Sci., Islam. Repub. Iran 22 (2011), 153-157. MR 2884149 |
| Reference:
|
[13] Lashkaripour, R., Talebi, G.: Lower bound for the norm of lower triangular matrices on block weighted sequence spaces.J. Math. Inequal. 5 (2011), 33-38. Zbl 1211.26018, MR 2799056, 10.7153/jmi-05-04 |
| Reference:
|
[14] Lashkaripour, R., Talebi, G.: Bounds for the operator norms of some Nörlund matrices on weighted sequence spaces.Preprint. |
| . |
