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

Lashkaripour, Rahmatollah, and Talebi, Gholomraza. "Lower bound and upper bound of operators on block weighted sequence spaces." Czechoslovak Mathematical Journal 62.2 (2012): 293-304. <http://eudml.org/doc/246225>.

@article{Lashkaripour2012,
abstract = {Let $A=(a_\{n,k\})_\{n,k\ge 1\}$ be a non-negative matrix. Denote by $L_\{v,p,q,F\}(A)$ the supremum of those $L$ that satisfy the inequality \[ \Vert Ax\Vert \_\{v,q,F\} \ge L\Vert x\Vert \_\{v,p,F\}, \] where $x\ge 0$ 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 $0<q\le p\le 1$. Another purpose of this paper is to establish a lower bound for $\Vert A_\{W\}^\{NM\} \Vert _\{v,p,F\}$, where $A_\{W\}^\{NM\}$ is the Nörlund matrix associated with the sequence $W=\lbrace w_n\rbrace _\{n=1\}^\infty $ and $1<p<\infty $. Our results generalize some works of Bennett, Jameson and present authors.},
author = {Lashkaripour, Rahmatollah, Talebi, Gholomraza},
journal = {Czechoslovak Mathematical Journal},
keywords = {lower bound; weighted sequence space; Hausdorff matrices; Euler matrices; Cesàro matrices; Hölder matrices; Gamma matrices; weighted sequence space; Hausdorff matrix; Euler matrix; Cesàro matrix; Hölder matrix; Gamma matrix},
language = {eng},
number = {2},
pages = {293-304},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Lower bound and upper bound of operators on block weighted sequence spaces},
url = {http://eudml.org/doc/246225},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Lashkaripour, Rahmatollah
AU - Talebi, Gholomraza
TI - Lower bound and upper bound of operators on block weighted sequence spaces
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 2
SP - 293
EP - 304
AB - Let $A=(a_{n,k})_{n,k\ge 1}$ be a non-negative matrix. Denote by $L_{v,p,q,F}(A)$ the supremum of those $L$ that satisfy the inequality \[ \Vert Ax\Vert _{v,q,F} \ge L\Vert x\Vert _{v,p,F}, \] where $x\ge 0$ 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 $0<q\le p\le 1$. Another purpose of this paper is to establish a lower bound for $\Vert A_{W}^{NM} \Vert _{v,p,F}$, where $A_{W}^{NM}$ is the Nörlund matrix associated with the sequence $W=\lbrace w_n\rbrace _{n=1}^\infty $ and $1<p<\infty $. Our results generalize some works of Bennett, Jameson and present authors.
LA - eng
KW - lower bound; weighted sequence space; Hausdorff matrices; Euler matrices; Cesàro matrices; Hölder matrices; Gamma matrices; weighted sequence space; Hausdorff matrix; Euler matrix; Cesàro matrix; Hölder matrix; Gamma matrix
UR - http://eudml.org/doc/246225
ER -