An inequality of multiple integral of $s$ norm of vectors in $\mathbb{R}^n$

TL;DR

This paper introduces new inequalities involving multiple integrals of vector norms in  space, utilizing a novel local product concept to establish these results.

Contribution

It presents new inequalities for multiple integrals of vector norms and introduces the local product notion to aid in the proofs.

Findings

Established new inequalities for multiple integrals of vector norms.

Introduced the concept of local product on a sheet and associated space.

Provided mathematical proofs leveraging the local product concept.

Abstract

In this paper, we prove some new inequalities. To facilitate this proof, we introduce the notion of the local product on a sheet and associated space.