Lower bounds of Copson type for the transposes of lower triangular matrices

Abstract

Let A = (a n,k ) n,k 0 be a non-negative matrix. Denote by L p,q (A) the supremum of those L satisfying the following inequality:

Approximation of lower bound for matrix operators on the weighted sequence space $C_{p}^r(w)(p \in (0,1))$

“…In this section, we focus on the evaluation of L p(w),C r q (w) (A t ), where 0 < q ≤ p < 1 and A is a non-negative lower triangular matrix. Our result gives a lower estimate for this value in terms of the constant M which is defined by Chen and Wang in [4], as:…”