Multipliers on Generalized Mixed Norm Sequence Spaces

Abstract EN

Given 1 ≤ p , q ≤ ∞ and sequences of integers ( n k ) k and ( n k ′ ) k such that n k ≤ n k ′ ≤ n k + 1 , the generalized mixed norm space ℓ ℐ ( p , q ) is defined as those sequences ( a j ) j such that ( ( ∑ j ∈ I k | a j | p ) 1 / p ) k ∈ ℓ q where I k = { j ∈ ℕ 0 s .

t .

n k ≤ j < n k ′ } , k ∈ ℕ 0 .

The necessary and sufficient conditions for a sequence λ = ( λ j ) j to belong to the space of multipliers ( ℓ ℐ ( r , s ) , ℓ ? ( u , v ) ) , for different sequences ℐ and ? of intervals in ℕ 0 , are determined.