@article {
author = {Moazzen, A. R. and Lashkaripour, R.},
title = {Some inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {3},
number = {1},
pages = {45-54},
year = {2012},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {},
doi = {10.22075/ijnaa.2012.46},
abstract = {Let $A=(a_{n,k})_{n,k\geq1}$ and $B=(b_{n,k})_{n,k\geq1}$ be two non-negative matrices. Denote by $L_{v,p,q,B}(A)$, the supremum of those $L$, satisfying the following inequality:$$\|Ax\|_{v,B(q)}\geq L\|x\|_{v,B(p)},$$where $x\geq 0$ and $x \in l_p(v,B)$ and also$v = (v_n)_{n=1}^\infty$ is an increasing, non-negative sequence of real numbers. In this paper, we obtain a Hardy-type formula for $L_{v,p,q,B}(H_\mu)$, where $H_\mu$ is the Hausdorff matrix and $0 < q \leq p \leq1$. Also for the case $p = 1$, we obtain $\|Ax\|_{v,B(1)}$, and for the case $p\geq 1$, we obtain $L_{v,p,q,B}(A)$.},
keywords = {Lower bound,Weighted block sequence space,Hausdorff matrices,Euler matrices,Cesaro matrices,Matrix norm},
url = {https://ijnaa.semnan.ac.ir/article_46.html},
eprint = {https://ijnaa.semnan.ac.ir/article_46_a875762021951bf010efadf9db780be0.pdf}
}