Exact norm estimates for multivariate dilation operators between two Bilateral Weight Grand Lebesgue Spaces

TL;DR

This paper provides precise norm estimates for multivariate dilation operators acting between weighted Lebesgue-Riesz and Grand Lebesgue Spaces, including examples and analysis of their compactness.

Contribution

It introduces sharp bounds for multivariate dilation operators between weighted Lebesgue-Riesz and Grand Lebesgue Spaces, extending previous results with new estimates and compactness analysis.

Findings

Sharp norm estimates for dilation operators derived

Examples illustrating the estimates provided

Analysis of operator compactness included

Abstract

We give in this short paper a sharp estimate for the norm of a multivariate dilation operator generated by multi-matrix (tensor) linear argument transformation (dilation operator) between two different weight Lebesgue-Riesz and Grand Lebesgue Spaces(GLS). We consider also some examples and study the compactness of these operators.