Tensor, Sobolev, Multiplicative and Convolution Operators in the Bide - Side Grand Lebesque Spaces

TL;DR

This paper investigates various inequalities involving tensor, Sobolev, multiplicative, and convolution operators within Bide-Side Grand Lebesgue Spaces, providing examples to demonstrate the sharpness of these inequalities.

Contribution

It introduces and analyzes inequalities for these operators in Bide-Side Grand Lebesgue Spaces, highlighting their optimal bounds with concrete examples.

Findings

Established sharp multiplicative inequalities

Derived convolution inequalities with optimal bounds

Provided examples demonstrating the sharpness of results

Abstract

In this paper we study the multiplicative, tensor, Sobolev's and convolution inequalities in certain Banach spaces, the so-called Bide - Side Grand Lebesque Spaces, and give examples to show their sharpness.