Symmetrization, factorization and arithmetic of quasi-Banach function spaces

TL;DR

This paper explores the relationships and operations involving symmetrizations of quasi-Banach function spaces, providing new insights into their structure, multipliers, and factorization methods.

Contribution

It establishes that symmetrization commutes with key constructions like Calderon-Lozanovskii spaces and pointwise products, and characterizes multipliers between Lorentz and Cesaro spaces.

Findings

Symmetrization commutes with certain space constructions.

Identified spaces of pointwise multipliers between Lorentz and Cesaro spaces.

Developed methods serve as an arithmetic framework for quasi-Banach function spaces.

Abstract

We investigate relations between symmetrizations of quasi-Banach function spaces and constructions such as Calderon-Lozanovskii spaces, pointwise product spaces and pointwise multipliers. We show that under reasonable assumptions the symmetrization commutes with these operations. We determine also the spaces of pointwise multipliers between Lorentz spaces and Cesaro spaces. Developed methods may be regarded as an arithmetic of quasi-Banach function spaces and proofs of Theorems 3, 4 and 6 give a kind of tutorial for these methods. Finally, the above results will be used in proofs of some factorization results.