An extension of Nikishin's factorization theorem

TL;DR

This paper extends Nikishin's factorization theorem by providing a new characterization of bounded sets in weak-type Lebesgue spaces and deriving novel factorizations for linear and multilinear operators.

Contribution

It introduces a Nikishin-Maurey type characterization for weak Lebesgue spaces and develops new operator factorizations.

Findings

New characterization of bounded subsets in weak Lebesgue spaces.

Derived factorizations for linear operators.

Extended results to multilinear operators.

Abstract

A Nikishin-Maurey characterization is given for bounded subsets of weak-type Lebesgue spaces. New factorizations for linear and multilinear operators are shown to follow.