Weighted Grand Lebesgue Spaces norm estimation for Hardy-Sobolev-Poincare-Wirtinger operators

TL;DR

This paper extends classical Hardy-Sobolev-Poincare-Wirtinger inequalities to Grand Lebesgue spaces, providing precise constant evaluations to enhance the understanding of these inequalities in more general functional spaces.

Contribution

It introduces the extension of Hardy-Sobolev-Poincare-Wirtinger inequalities to Grand Lebesgue spaces with exact constants, advancing the theoretical framework.

Findings

Extended inequalities to Grand Lebesgue spaces

Provided exact constants for the inequalities

Enhanced understanding of functional space embeddings

Abstract

We extend the classical Hardy-Sobolev-Poincare-Wirtinger inequalities from the ordinary Lebesgue-Riesz spaces into the Grand Lebesgue ones, with exact constants evaluation.