Sharp value for the norm of composition and multiplicative operators between two different Grand Lebesgue spaces

TL;DR

This paper derives exact formulas for the norms of composition, multiplicative, and product operators acting between different Lebesgue-Riesz and Grand Lebesgue spaces, enhancing understanding of their boundedness.

Contribution

It provides the first precise expressions for these operator norms between diverse Lebesgue and Grand Lebesgue spaces, using constructed examples.

Findings

Exact operator norms are obtained for various transformations.

The results clarify the boundedness conditions between different function spaces.

New formulas facilitate analysis of operators in advanced functional spaces.

Abstract

We calculate in this paper the norm of composition, multiplicative and product operator, generated by multiplicative and measurable argument transformation between two different ordinary Lebesgue-Riesz and Grand Lebesgue spaces. We set ourselves the aim to obtain the exact expression for the norm of the considered operators by means of building of appropriate examples.