Multipliers on Generalized Mixed Norm Sequence Spaces

Abstract

Given 1≤p,q≤∞ and sequences of integers (nk)k and (nk′)k such that nk≤nk′≤nk+1, the generalized mixed norm space ℓℐ(p,q) is defined as those sequences (aj)j such that ((∑j∈Ik‍|aj|p)1/p)k∈ℓq where Ik={j∈ℕ0 s.t. nk≤j<nk′}, k∈ℕ0. The necessary and sufficient conditions for a sequence λ=(λj)j to belong to the space of multipliers (ℓℐ(r,s),ℓ𝒥(u,v)), for different sequences ℐ and 𝒥 of intervals in ℕ0, are determined.