%0 Journal Article
%T Some inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Moazzen, A. R.
%A Lashkaripour, R.
%D 2012
%\ 01/01/2012
%V 3
%N 1
%P 45-54
%! Some inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm
%K Lower bound
%K Weighted block sequence space
%K Hausdor matrices
%K Euler matrices
%K Cesaro matrices
%K Matrix norm
%R 10.22075/ijnaa.2012.46
%X Let A = (an;k)n;k1 and B = (bn;k)n;k1 be two non-negative ma-trices. Denote by Lv;p;q;B(A), the supremum of those L, satisfying the followinginequality:k Ax kv;B(q) L k x kv;B(p);where x 0 and x 2 lp(v;B) and also v = (vn)1n=1 is an increasing, non-negativesequence of real numbers. In this paper, we obtain a Hardy-type formula forLv;p;q;B(H), where H is the Hausdor matrix and 0 < q p 1. Also for thecase p = 1, we obtain kAkw;B(1), and for the case p 1, we obtain Lw;B(p)(A).
%U https://ijnaa.semnan.ac.ir/article_46_a875762021951bf010efadf9db780be0.pdf