Lower bound and upper bound of operators on block weighted sequence spaces

Title:

Lower bound and upper bound of operators on block weighted sequence spaces

Creator:

Rahmatollah and Talebi, Gholomraza

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:bf3c0097-ca1c-43ab-8aed-fbde3e302b35
uuid:bf3c0097-ca1c-43ab-8aed-fbde3e302b35

Subject:

lower bound, weighted sequence space, Hausdorff matrices, Euler matrices, Cesàro matrices, Hölder matrices, and Gamma matrices

Type:

model:article and TEXT

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

293-304

Source:

Czechoslovak Mathematical Journal | 2012 Volume:62 | Number:2

Harvested from:

CDK

Metadata only:

false