Pointwise multipliers of Orlicz function spaces and factorization

TL;DR

This paper characterizes the space of pointwise multipliers between Orlicz spaces as another Orlicz space and provides conditions for their factorization, advancing the understanding of these function spaces.

Contribution

It offers a new representation of multiplier spaces between Orlicz spaces and derives criteria for their factorization, which was previously not well-understood.

Findings

Multiplier space between two Orlicz spaces is another Orlicz space with a specific Young function

Derived explicit formula for the Young function generating the multiplier space

Established necessary and sufficient conditions for factorization of Orlicz spaces

Abstract

In the paper we find representation of the space of pointwise multipliers between two Orlicz function spaces, which appears to be another Orlicz space and the formula for the Young function generating this space is given. Further, we apply this result to find necessary and suffcient conditions for factorization of Orlicz function spaces.