Sharp Weight Hardy-Sobolev inequalities for Grand Lebesgue Spaces

TL;DR

This paper determines the exact norms of Hardy-Sobolev type operators acting between weighted Grand Lebesgue Spaces in multidimensional Euclidean space, providing precise operator bounds.

Contribution

It introduces exact norm calculations for Hardy-Sobolev operators in weighted Grand Lebesgue Spaces, advancing the understanding of these operators in functional analysis.

Findings

Exact norms of Hardy-Sobolev operators are computed.

Results apply to multidimensional Euclidean spaces.

Provides a basis for further analysis of operators in GLS.

Abstract

We give in this short paper the exact value for norms of two operators of Hardy-Sobolev type acting between two weight Grand Lebesgue Space (GLS) based on the whole multidimensional Euclidean space.