Abstract
(Communicated by R. Oinarov) Abstract. Let 1 < p < ∞ and A =( an,k)n,k1 be a non-negative matrix. Denote byAw,p,F , the infimum of those U satisfying the following inequality: � Axw,p,F Uxw,p,I , where x 0a ndx ∈ lp(w,I) and also w =( wn) ∞=1 is a decreasing, non-negative sequence of real numbers. The purpose of this paper is to give a lower bound forAw,p,F ,w hereA is a lower triangular matrix. In particular, we apply our results to Weighted mean matrices and Norlund matrices which recently considered in (2,3,6) on the usual sequence spaces. Our results generalize some work of Jameson, Lashkaripour, Frotannia and Chen in (4,7,8).
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