Hardy-Littlewood inequalities for norms of positive operators on sequence spaces

TL;DR

This paper improves estimates of Hardy-Littlewood inequalities for positive operators on sequence spaces using Maurey's factorization, providing simplified proofs and enhanced bounds.

Contribution

It introduces improved Hardy-Littlewood estimates for positive operators on sequence spaces by applying Maurey's factorization, simplifying existing proofs and strengthening bounds.

Findings

Enhanced bounds for positive operators on sequence spaces.

Simplified proofs of Hardy-Littlewood inequalities.

Application of Maurey's factorization to improve estimates.

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.