Abstract
We consider estimates of Hardy and Littlewood for norms of operators on sequence spaces, and we apply a factorization result of Maurey to obtain improved estimates and simplified proofs for the special case of a positive operator.
Highlights
In 1934, Hardy and Littlewood [1], using powerful but technically difficult methods, extended results of Littlewood [2] and Toeplitz [4] to give lower bounds for norms of bilinear forms on sequence spaces
We prove Theorem 1 and Theorem 2 for the special case of an operator with non negative entries
A p,q = inf d r · B p,p, where the infimum is taken over all possible factorizations
Summary
In 1934, Hardy and Littlewood [1], using powerful but technically difficult methods, extended results of Littlewood [2] and Toeplitz [4] to give lower bounds for norms of bilinear forms on sequence spaces. If 1 ≤ p < ∞, we write p for the complex vector space of all complex sequences x = (xk) such that x p: = We write c0 for the space of all null complex sequences x = (xk) with the norm x ∞ : = sup |xk|.
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