Multipliers on Generalized Mixed Norm Sequence Spaces

Given 1 <= p,q <= infinity and sequences of integers (n(k))(k) and (n(k)(l))(k) such that n(k) <= n(k)(l) <= n(k+1), the generalized mixed norm space l(j) (p,q) is defined as those sequences (a(j))(j) such that ((Sigma(j epsilon Ik)vertical bar a(j)vertical bar(p))(1/p))(k) epsilon l(q) where I-k = {j epsilon N-0 s.t. n(k) <= j < n(k)(l)}, k epsilon N-0. The necessary and sufficient conditions for a sequence lambda= (lambda(j))(j) to belong to the space of multipliers (l(j) (r,s), l(j) (u,v), for different sequences J and J of intervals in N-0, are determined.