LOWER BOUND OF COPSON TYPE FOR N¨ORLUND MATRIX

Let A = (an;k)n;k¸0 be a non-negative matrix. Denote by Lp;q(A) the supremum of those L satisfying kAXkq ¸ LkXkp (X 2 `p;X ¸ 0): We derive a range for the value of Lp;q(ANM W ) Where 0 < q · p < 1 and ANM W denotes the N¨orlund matrix associated with the weight function W. The case Lp;q((ANM W ) t) with ¡1 < p; q < 0 is also investigated.