Moazzen, A., Lashkaripour, R. (2012). Some inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm. International Journal of Nonlinear Analysis and Applications, 3(1), 45-54. doi: 10.22075/ijnaa.2012.46

A. R. Moazzen; R. Lashkaripour. "Some inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm". International Journal of Nonlinear Analysis and Applications, 3, 1, 2012, 45-54. doi: 10.22075/ijnaa.2012.46

Moazzen, A., Lashkaripour, R. (2012). 'Some inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm', International Journal of Nonlinear Analysis and Applications, 3(1), pp. 45-54. doi: 10.22075/ijnaa.2012.46

Moazzen, A., Lashkaripour, R. Some inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm. International Journal of Nonlinear Analysis and Applications, 2012; 3(1): 45-54. doi: 10.22075/ijnaa.2012.46

Some inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm

^{}Dept. of Math.,University of Sistan and Baluchestan , Zahedan, Iran.

Abstract

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 following inequality: 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-negative sequence of real numbers. In this paper, we obtain a Hardy-type formula for Lv;p;q;B(H), where H is the Hausdor matrix and 0 < q p 1. Also for the case p = 1, we obtain kAkw;B(1), and for the case p 1, we obtain Lw;B(p)(A).