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\section*{ Bounds for matrices on weighted sequence spaces } By {D. Foroutannia}.  

\medskip  \noindent  Let $w=(w_n)$ be a decreasing non-negative sequence and  $F$ be a partition of positive integers. If $F=(F_n)$,  where each $F_n$ is a finite interval of positive integers and also for all $n$, $\max{F_n}<\min{F_{n+1}}$.  The block weighted sequence space $l_p(w,F)$ is the space of all real sequences $x=(x_n)$ with  $$\|x\|_{p,w,F}=\left(\sum_{n=1}^{\infty}w_n|<x,F_n>|^p\right)^{1/p}<\infty,$$  where $<x,F_n>=\sum_{i\in F_n}x_i$. \\ In this paper, we consider inequalities of the form $\|Ax\|_{p,w,F}\le L\|Bx\|_{q,v,F}$, where $A$ and $B$ are matrix operators, $x$ decreasing non-negative sequence and $w$, $v$ are weights and also $F$ is a block. Moreover, this study is an extension of some works of which are studied before on sequence spaces $l_{p}(v)$ by J. Pecaric, I. Peric and R. Roki in [3].
%Inequality; Lower bound; Upper bound; Block weighted sequence spaces;  Copson matrix","","","","11:58:03","Wed Mar 05 2008","217.219.28.191"
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