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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: 2016-04-07
Stable URL:
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