Abstract
In this paper we prove a new discrete Hardy type inequality involving a kernel which has a more general form than those known in the literature. We obtain necessary and sufficient conditions for the boundedness of a matrix operator from the weighted $l_{p,v}$ space into the weighted $l_{q, u}$ space defined by $\left(Af\right)_j:=\sum\limits_{i=j}^\infty a_{i,j}f_i,$ for all $f=\{f_i\}_{i=1}^{\infty} \in l_{p,v}$ in case $q,p\in (1,\infty)$ with $q$ less than $p$, and $a_{i, j}\geq 0$. Then we deduce a corresponding dual statement.
Citation
Zhanar Taspaganbetova. Ainur Temirkhanova. "Criteria on boundedness of matrix operators in weighted spaces of sequences andtheir applications." Ann. Funct. Anal. 2 (1) 114 - 127, 2011. https://doi.org/10.15352/afa/1399900267
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