Certain Results For a Class of Nonlinear Functional Spaces

TL;DR

This paper investigates properties of a specific class of nonlinear functional spaces, called pn-spaces, establishing integral inequalities and relations to Lebesgue and Sobolev spaces, relevant for nonlinear differential equations.

Contribution

It introduces and analyzes pn-spaces, revealing their connections to classical functional spaces and providing foundational inequalities and theorems.

Findings

Established integral inequalities for pn-spaces

Proved relations between pn-spaces and Lebesgue/Sobolev spaces

Analyzed properties of pn-spaces with constant and variable exponents

Abstract

In this article, we study the properties of a class of functional spaces which arise from the investigation of nonlinear differential equations. We establish some integral inequalities then by applying these inequalities, we prove some lemmas and theorems, which indicate the relation of these spaces (pn-spaces) with the Lebesgue and Sobolev spaces in the case when pn-spaces with constant and variable exponents.