Weighted Hardy-Littlewood average operators on bilateral grand Lebesgue spaces

TL;DR

This paper derives precise bounds for weighted Hardy-Littlewood average operators in Bilateral Grand Lebesgue Spaces, demonstrating the sharpness of these inequalities through examples.

Contribution

It provides the first non-asymptotic exact norm estimates for these operators in Bilateral Grand Lebesgue Spaces, including sharpness validation.

Findings

Exact norm estimations for weighted Hardy-Littlewood operators

Sharpness of inequalities demonstrated with examples

Extension of operator bounds to Bilateral Grand Lebesgue Spaces

Abstract

We obtain in this short article the non-asymptotic exact estimations for the norm of (generalized) weighted Hardy-Littlewood average integral operator in the so-called Bilateral Grand Lebesgue Spaces. We also give examples to show the sharpness of these inequalities.