Generalized Grand Lebesgue Spaces norm estimations for some operators

TL;DR

This paper investigates norm estimates for operators acting between moment rearrangement invariant spaces, including generalized Grand Lebesgue Spaces, using fundamental functions to formulate bounds.

Contribution

It introduces a framework for estimating operator norms between these spaces, extending previous results to non-linear operators and broadening the applicability.

Findings

Derived norm estimates for operators in generalized Grand Lebesgue Spaces

Established bounds in terms of fundamental functions of the spaces

Extended analysis to non-linear operators in rearrangement invariant spaces

Abstract

We study moment rearrangement invariant spaces, which contain as particular cases the generalized Grand Lebesgue Spaces, and provide norm estimates for some operators, not necessarily linear, acting between some measurable rearrangement invariant spaces. The estimations are formulated in the terms of fundamental functions for these spaces.