Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68223120120101Some inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm45544610.22075/ijnaa.2012.46ENA. R.MoazzenDept. of Math.,University of Sistan and Baluchestan , Zahedan, Iran.R.LashkaripourDept. of Math.,University of Sistan and Baluchestan , Zahedan, Iran.Journal Article20110106Let A = (an;k)n;k1 and B = (bn;k)n;k1 be two non-negative ma-<br />trices. Denote by Lv;p;q;B(A), the supremum of those L, satisfying the following<br />inequality:<br />k Ax kv;B(q) L k x kv;B(p);<br />where x 0 and x 2 lp(v;B) and also v = (vn)1n<br />=1 is an increasing, non-negative<br />sequence of real numbers. In this paper, we obtain a Hardy-type formula for<br />Lv;p;q;B(H), where H is the Hausdor matrix and 0 < q p 1. Also for the<br />case p = 1, we obtain kAkw;B(1), and for the case p 1, we obtain Lw;B(p)(A).https://ijnaa.semnan.ac.ir/article_46_a875762021951bf010efadf9db780be0.pdf