Norm estimates in Grand Lebesgue Spaces for some operators, including magic square matrices

TL;DR

This paper extends norm estimates for integral and matrix operators from classical Lebesgue spaces to Grand Lebesgue Spaces, including applications to magic square matrices, broadening the scope of operator norm analysis.

Contribution

It introduces a general framework for estimating operator norms in Grand Lebesgue Spaces, including specific results for matrices generated by positive magic squares.

Findings

Extended classical norm estimates to Grand Lebesgue Spaces.

Provided explicit estimates for matrix operators from magic square matrices.

Demonstrated applicability to finite-dimensional Lebesgue spaces.

Abstract

We extend the classical Lebesgue-Riesz norm estimations for integral operators acting between different classical Lebesgue-Riesz spaces into the Grand Lebesgue Spaces, in the general case. As an example we consider matrix operators acting between finite dimensional Lebesgue-Riesz spaces, especially generated by means of positive magic squares.