Lower bounds for generalized Hausdorff matrices and lower triangular matrices on the block weighted sequence space ℓp(w, F)

Abstract

Let and be a non-negative matrix. Denote by , the supremum of those , satisfying the following inequalitywhere is a partition of positive integers, , is a non-negative sequence in and is a monotone and non-negative sequence of real number. In this paper a Hardy-type formula is obtained for , where is the generalized Hausdorff matrix, and Another purpose of this paper is to establish a general upper estimate for the exact value of , for which recently a lower estimate was established in Lashkaripour and Talebi [Lashkaripour R, Talebi G. Bull. Iran. Math. Soc. 2011;37:115–126], where is a non-negative lower triangular matrix and . We also derive the corresponding result for with In particular, we apply our results to summability matrices, weighted mean matrices, Nörlund matrices. Our results also generalize some results in Chen and Wang [Chen C-P, Wang K-Z. Linear Multilinear Algebra, March 2011;59:321–337] and Lashkaripour and Talebi [Lashkaripour R, Talebi G. Czech. Math. J. 2012; 62: 293–04.].